roadway safety design synthesis - texas a&m universityinterim roadway safety design workbook....

Technical Report Documentation . Report No.FHWA/TX-05/0-4703-P1

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and SubtitleROADWAY SAFETY DESIGN SYNTHESIS

5. Report DateMay 2005Resubmitted: September 2005Resubmitted: November 2005 6. Performing Organization Code

7. Author(s)J. Bonneson, K. Zimmerman, and K. Fitzpatrick

8. Performing Organization Report No.Product 0-4703-P1

9. Performing Organization Name and AddressTexas Transportation InstituteThe Texas A&M University SystemCollege Station, Texas 77843-3135

10. Work Unit No. (TRAIS)

11. Contract or Grant No.Project 0-4703

12. Sponsoring Agency Name and AddressTexas Department of TransportationResearch and Technology Implementation OfficeP.O. Box 5080Austin, Texas 78763-5080

13. Type of Report and Period CoveredProduct

14. Sponsoring Agency Code

15. Supplementary NotesProject performed in cooperation with the Texas Department of Transportation and the Federal HighwayAdministration.Project Title: Incorporating Safety into the Highway Design ProcessURL: http://tti.tamu.edu/documents/0-4703-P1.pdf16. Abstract

Highway safety is an ongoing concern to the Texas Department of Transportation (TxDOT). As part of itsproactive commitment to improving highway safety, TxDOT is moving toward including quantitative safetyanalyses earlier in the project development process. The objectives of this research project are: (1) thedevelopment of safety design guidelines and evaluation tools to be used by TxDOT designers, and (2) theproduction of a plan for the incorporation of these guidelines and tools in the planning and design stages ofthe project development process.

This document describes the effect of key design components on street and highway safety. The informationpresented herein represents the findings from a critical review of the literature and an evaluation of thereported safety trends and relationships. The purpose of this document is to promote the explicit andobjective consideration of safety in the design process. It is envisioned to be a reference document that willbe useful to engineers and researchers who desire detailed safety information on various highway geometricdesign elements. The information in this document was used to develop the guidelines presented in theInterim Roadway Safety Design Workbook.

17. Key WordsHighway Design, Highway Safety, Freeways, UrbanStreets, Rural Highways, Types of Intersections,Ramps (Interchanges)

18. Distribution Statement

19. Security Classif.(of this report) 20. Security Classif.(of this page) 21. No. of Pages 204

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

http://tti.tamu.edu/documents/0-4703-P1.pdf

ROADWAY SAFETY DESIGN SYNTHESIS

by

J. Bonneson, P.E.Research Engineer

Texas Transportation Institute

K. Zimmerman, P.E.Assistant Research Engineer


and

K. Fitzpatrick, P.E.Research Engineer


Product 0-4703-P1Project Number 0-4703

Project Title: Incorporating Safety into the Highway Design Process

Performed in cooperation with theTexas Department of Transportation

and theFederal Highway Administration

May 2005Resubmitted: September 2005Resubmitted: November 2005

TEXAS TRANSPORTATION INSTITUTEThe Texas A&M University SystemCollege Station, Texas 77843-3135

v

DISCLAIMER

The contents of this report reflect the views of the authors, who are responsible for the factsand the accuracy of the data published herein. The contents do not necessarily reflect the officialview or policies of the Federal Highway Administration (FHWA) and/or the Texas Department ofTransportation (TxDOT). This report does not constitute a standard, specification, or regulation.It is not intended for construction, bidding, or permit purposes. The engineer in charge of the projectwas James Bonneson, P.E. #67178.

NOTICE

The United States Government and the State of Texas do not endorse products ormanufacturers. Trade or manufacturers’ names appear herein solely because they are consideredessential to the object of this report.

vi

ACKNOWLEDGMENTS

This research project was sponsored by the Texas Department of Transportation and theFederal Highway Administration. The research was conducted by Dr. James Bonneson,Dr. Karl Zimmerman, and Dr. Kay Fitzpatrick with the Texas Transportation Institute.

The researchers would like to acknowledge the support and guidance provided by the ProjectMonitoring Committee:

! Ms. Aurora (Rory) Meza, Project Coordinator (TxDOT);! Ms. Elizabeth Hilton, Project Director (TxDOT);! Mr. David Bartz (FHWA);! Mr. Mike Battles (TxDOT);! Mr. Stan Hall (TxDOT);! Mr. Richard Harper (TxDOT); ! Ms. Meg Moore (TxDOT); and! Ms. Joanne Wright (TxDOT).

In addition, the researchers would like to acknowledge the valuable assistance provided byMr. Michael P. Pratt during the report preparation and review stages.

vii

TABLE OF CONTENTS

Page

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3HIGHWAY SAFETY AND GEOMETRIC DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3ROLE OF SAFETY-CONSCIOUS DESIGN IN THE TxDOT DESIGN PROCESS . . . . 1-6PURPOSE AND ORGANIZATION OF THE SYNTHESIS . . . . . . . . . . . . . . . . . . . . . . . 1-9REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10

CHAPTER 2. FREEWAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25

CHAPTER 3. RURAL HIGHWAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36

CHAPTER 4. URBAN STREETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33

CHAPTER 5. INTERCHANGE RAMPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16

viii

TABLE OF CONTENTS (Continued)

Page

CHAPTER 6. RURAL INTERSECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-34

CHAPTER 7. URBAN INTERSECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29

ix

LIST OF FIGURES

Figure Page

1-1 Components of the Project Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-72-1 Severe Crash Frequency for Urban Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-92-2 Severe Crash Frequency for Rural Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-102-3 Horizontal Curve AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-122-4 Grade AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-132-5 Lane Width AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-152-6 Outside Shoulder Width AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-162-7 Inside Shoulder Width AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-182-8 Relationship between Median Width and Severe Crash Frequency . . . . . . . . . . . . . . . 2-182-9 Median Width AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-192-10 Speed Limit AMF for Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-243-1 Severe Crash Frequency for Rural Two-Lane Highways . . . . . . . . . . . . . . . . . . . . . . . 3-103-2 Severe Crash Frequency for Rural Multilane Divided Highways . . . . . . . . . . . . . . . . . 3-103-3 Horizontal Curve AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-113-4 Grade AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-143-5 Lane Width AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-193-6 Lane Width AMF for Low Volume Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . 3-193-7 Outside Shoulder Width AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-213-8 Outside Shoulder Width AMF for Low Volume Rural Highways . . . . . . . . . . . . . . . . 3-213-9 Inside Shoulder Width AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-233-10 Relationship between Median Width and Severe Crash Frequency . . . . . . . . . . . . . . . 3-233-11 Median Width AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-243-12 TWLTL Median Type AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-263-13 Correlation between Relative Bridge Width and Bridge Crash Rate . . . . . . . . . . . . . . 3-313-14 Driveway Density AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-343-15 Speed Limit AMF for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-364-1 Severe Crash Frequency for Undivided Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-134-2 Severe Crash Frequency for Streets with TWLTL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-134-3 Severe Crash Frequency for Four-Lane Streets with Raised-Curb Median . . . . . . . . . 4-144-4 Curve Radius AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-154-5 Lane Width AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-174-6 Shoulder Width AMF for Two-Lane Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-184-7 Shoulder Width AMF for Four-Lane Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-194-8 Median Width AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-204-9 TWLTL Median Type AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-234-10 Parking AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-244-11 Driveway Density AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

x

LIST OF FIGURES (Continued)

Figure Page

4-12 Truck Presence AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-324-13 Speed Limit AMF for Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-335-1 Commonly Used Interchange Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-45-2 Basic Interchange Ramp Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-65-3 Severe Crash Frequency Predicted by Bauer and Harwood Model . . . . . . . . . . . . . . . . . 5-85-4 Comparison of Predicted and Reported Crash Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 5-115-5 Acceleration and Deceleration Speed-Change Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . 5-145-6 Crash Frequencies for Ramp Speed-Change Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-156-1 Comparison of Safety Prediction Models for Rural Signalized Intersections . . . . . . . . . 6-86-2 Comparison of Safety Prediction Models for Rural Unsignalized Intersections . . . . . . 6-126-3 Correlation between Model Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-136-4 Driveway Frequency AMF for Rural Signalized Intersections . . . . . . . . . . . . . . . . . . . 6-216-5 Truck Presence AMF for Rural Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . 6-226-6 Speed AMF for Rural Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-246-7 Shoulder Width AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . 6-276-8 Median Width AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . 6-286-9 Skew Angle AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . 6-306-10 Driveway Frequency AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . 6-326-11 Truck Presence AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . 6-336-12 Speed AMF for Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-347-1 Crash Models Developed by Lyon et al. for Four-Leg Intersections . . . . . . . . . . . . . . . . 7-77-2 Crash Models Developed by Lyon et al. for Three-Leg Intersections . . . . . . . . . . . . . . . 7-77-3 Comparison of Safety Prediction Models for Urban Signalized Intersections . . . . . . . 7-117-4 Comparison of Safety Prediction Models for Urban Unsignalized Intersections . . . . . 7-157-5 Correlation between Model Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-167-6 Lane Width AMF for Urban Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . 7-217-7 Speed AMF for Urban Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-227-8 Lane Width AMF for Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . 7-257-9 Shoulder Width AMF for Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . 7-267-10 Median Width AMF for Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . 7-287-11 Speed AMF for Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29

xi

LIST OF TABLES

Table Page

1-1 National Motor Vehicle Crash Statistics for 1995 and 2000 . . . . . . . . . . . . . . . . . . . . . . 1-41-2 Comparison of Texas with National Motor Vehicle Crash Statistics . . . . . . . . . . . . . . . 1-51-3 Potential Safety Tasks in the Project Development Process . . . . . . . . . . . . . . . . . . . . . . 1-82-1 Database Characteristics for Various Freeway Safety Prediction Models . . . . . . . . . . . 2-62-2 Typical Values Used for Freeway Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 2-92-3 AMFs Related to Geometric Design of Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-102-4 Coefficient Values for Grade on Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-132-5 Crash Distribution for Freeway Lane Width AMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-152-6 Crash Distribution for Freeway Outside Shoulder Width AMF . . . . . . . . . . . . . . . . . . 2-162-7 Crash Distribution for Freeway Inside Shoulder Width AMF . . . . . . . . . . . . . . . . . . . 2-172-8 Coefficient Values for Median Width on Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-192-9 AMFs for Shoulder Rumble Strips on Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-202-10 Crash Distribution for Freeway Shoulder Rumble Strip AMF . . . . . . . . . . . . . . . . . . . 2-202-11 AMFs Related to Roadside Design of Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-212-12 Coefficient Values for Utility Pole Density along Freeways . . . . . . . . . . . . . . . . . . . . . 2-222-13 Crash Distribution for Freeway Utility Pole Density AMF . . . . . . . . . . . . . . . . . . . . . . 2-222-14 RSAP Input Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-232-15 Coefficient Values for Speed Limit on Freeways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-243-1 Database Characteristics for Rural Two-Lane Highway Safety Prediction Models . . . . 3-63-2 Database Characteristics for Rural Multilane Highway Safety Prediction Models . . . . . 3-73-3 Typical Values Used for Rural Highway Model Comparison . . . . . . . . . . . . . . . . . . . . . 3-93-4 AMFs Related to Geometric Design of Rural Highways . . . . . . . . . . . . . . . . . . . . . . . 3-103-5 Crash Rate Analysis for Various Rural Highway Cross Sections . . . . . . . . . . . . . . . . . 3-133-6 Coefficient Values for Grade on Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-153-7 Coefficient Analysis for Lane and Shoulder Width on Rural Highways . . . . . . . . . . . . 3-163-8 Crash Distribution for Rural Highway Lane Width AMF . . . . . . . . . . . . . . . . . . . . . . . 3-183-9 Crash Distribution for Rural Highway Outside Shoulder Width AMF . . . . . . . . . . . . . 3-203-10 Crash Distribution for Rural Highway Inside Shoulder Width AMF . . . . . . . . . . . . . . 3-223-11 Coefficient Values for Median Width on Rural Highways . . . . . . . . . . . . . . . . . . . . . . 3-243-12 AMFs for Shoulder Rumble Strips on Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . 3-253-13 Crash Distribution for Rural Highway Shoulder Rumble Strip AMF . . . . . . . . . . . . . . 3-253-14 AMFs for Centerline Rumble Strip on Rural Two-Lane Highways . . . . . . . . . . . . . . . 3-253-15 AMFs for Superelevation on Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-273-16 AMFs for Passing Lanes on Rural Two-Lane Highways . . . . . . . . . . . . . . . . . . . . . . . 3-273-17 AMFs Related to Roadside Design of Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . 3-283-18 Coefficient Values for Horizontal Clearance on Rural Highways . . . . . . . . . . . . . . . . 3-293-19 Crash Distribution for Rural Highway Horizontal Clearance Width AMF . . . . . . . . . . 3-293-20 Coefficient Values for Side Slope on Rural Highways . . . . . . . . . . . . . . . . . . . . . . . . . 3-29

xii

LIST OF TABLES (Continued)

Table Page

3-21 Coefficient Values for Utility Pole Density on Rural Highways . . . . . . . . . . . . . . . . . . 3-303-22 Crash Distribution for Rural Highway Utility Pole Density AMF . . . . . . . . . . . . . . . . 3-303-23 Coefficient Values for Bridge Width on Rural Highways . . . . . . . . . . . . . . . . . . . . . . . 3-313-24 Crash Distribution for Rural Highway Bridge Width AMF . . . . . . . . . . . . . . . . . . . . . 3-313-25 RSAP Input Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-323-26 Coefficient Values for Driveway Density for Rural Highways . . . . . . . . . . . . . . . . . . . 3-333-27 Coefficient Values for Speed Limit for Rural Highways . . . . . . . . . . . . . . . . . . . . . . . 3-354-1 Base Crash Rates and Adjustment Factors Reported by Harwood . . . . . . . . . . . . . . . . . 4-54-2 Database Characteristics for Various Safety Prediction Models . . . . . . . . . . . . . . . . . . . 4-64-3 Typical Values Used for Urban Street Model Comparison . . . . . . . . . . . . . . . . . . . . . . 4-124-4 AMFs Related to Geometric Design of Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . 4-144-5 Crash Distribution for Urban Street Lane Width AMF . . . . . . . . . . . . . . . . . . . . . . . . . 4-174-6 Crash Distribution for Urban Street Shoulder Width AMF . . . . . . . . . . . . . . . . . . . . . 4-184-7 Coefficient Values for Median Width on Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . 4-204-8 Before-After TWLTL Crash Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-224-9 AMFs for Parallel Parking on Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-234-10 Comparison of Angle Parking with Parallel Parking . . . . . . . . . . . . . . . . . . . . . . . . . . 4-254-11 Coefficient Values for Uncurbed Cross Section on Urban Streets . . . . . . . . . . . . . . . . 4-264-12 AMFs for Uncurbed Cross Section on Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . 4-264-13 AMFs Related to Roadside Design of Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . 4-274-14 Coefficient Values for Utility Pole Offset on Urban Streets . . . . . . . . . . . . . . . . . . . . . 4-284-15 Crash Distribution for Urban Street Utility Pole Offset AMF . . . . . . . . . . . . . . . . . . . 4-284-16 RSAP Input Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-294-17 Coefficient Values for Speed Limit on Urban Streets . . . . . . . . . . . . . . . . . . . . . . . . . . 4-335-1 Crash Adjustment Factors for Equation 5-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-75-2 Severe Crash Rates Reported by Khorashadi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-95-3 Severe Crash Rates for Various Ramp Configurations . . . . . . . . . . . . . . . . . . . . . . . . . 5-125-4 Severe Crash Rate Analysis for Frontage-Road Ramps . . . . . . . . . . . . . . . . . . . . . . . . 5-136-1 Database Characteristics for Signalized Intersection Safety Prediction Models . . . . . . . 6-66-2 Typical Values Used for Rural Signalized Intersection Model Comparison . . . . . . . . . . 6-76-3 Database Characteristics for Unsignalized Intersection Safety Prediction Models . . . . 6-106-4 Typical Values Used for Rural Unsignalized Intersection Model Comparison . . . . . . 6-116-5 Severe Crash Rates for Three-Leg Rural Intersections . . . . . . . . . . . . . . . . . . . . . . . . . 6-146-6 Severe Crash Rates for Four-Leg Rural Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . 6-156-7 AMFs Related to Geometric Design of Rural Signalized Intersections . . . . . . . . . . . . 6-166-8 Effect of Adding a Left-Turn Lane at a Rural Signalized Intersection . . . . . . . . . . . . . 6-166-9 AMFs for Excluding a Left-Turn Lane at a Rural Signalized Intersection . . . . . . . . . . 6-16

xiii

LIST OF TABLES (Continued)

Table Page

6-10 AMFs for Adding a Right-Turn Lane at a Rural Signalized Intersection . . . . . . . . . . . 6-176-11 AMFs for Number of Through Lanes at Rural and Urban Signalized Intersections . . . 6-186-12 Coefficient Analysis for Driveway Frequency at Rural Intersections . . . . . . . . . . . . . . 6-206-13 Coefficient Analysis for Truck Presence at Rural Signalized Intersections . . . . . . . . . 6-226-14 Coefficient Analysis for Speed at Rural and Urban Intersections . . . . . . . . . . . . . . . . . 6-236-15 AMFs Related to Geometric Design of Rural Unsignalized Intersections . . . . . . . . . . 6-236-16 AMFs for Adding a Left-Turn Lane at a Rural Unsignalized Intersection . . . . . . . . . . 6-256-17 AMFs for Adding a Right-Turn Lane at a Rural Unsignalized Intersection . . . . . . . . . 6-256-18 AMFs for Number of Through Lanes at Rural Unsignalized Intersections . . . . . . . . . 6-266-19 AMFs for Median Presence at Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . 6-276-20 Coefficient Analysis for Median Width at Rural Unsignalized Intersections . . . . . . . . 6-286-21 Coefficient Analysis for Skew Angle at Rural Unsignalized Intersections . . . . . . . . . . 6-296-22 Coefficient Analysis for Truck Presence at Rural Unsignalized Intersections . . . . . . . 6-337-1 Calibration Coefficients for Lyon Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-67-2 Database Characteristics for Signalized Intersection Safety Prediction Models . . . . . . . 7-87-3 Calibration Coefficients for McGee Signalized Intersection Models . . . . . . . . . . . . . . . 7-97-4 Typical Values Used for Urban Signalized Intersection Model Comparison . . . . . . . . 7-107-5 Database Characteristics for Unsignalized Intersection Safety Prediction Models . . . . 7-137-6 Calibration Coefficients for McGee Unsignalized Intersection Models . . . . . . . . . . . . 7-137-7 Typical Values Used for Urban Unsignalized Intersection Model Comparison . . . . . . 7-147-8 Severe Crash Rates for Three-Leg Urban Intersections . . . . . . . . . . . . . . . . . . . . . . . . 7-177-9 Severe Crash Rates for Four-Leg Urban Intersections . . . . . . . . . . . . . . . . . . . . . . . . . 7-177-10 AMFs Related to Geometric Design of Urban Signalized Intersections . . . . . . . . . . . . 7-187-11 Effect of Adding a Left-Turn Lane at an Urban Signalized Intersection . . . . . . . . . . . . 7-197-12 AMFs for Excluding a Left-Turn Lane at an Urban Signalized Intersection . . . . . . . . 7-197-13 AMFs for Adding a Right-Turn Lane at an Urban Signalized Intersection . . . . . . . . . 7-207-14 AMFs for Number of Through Lanes at Urban Signalized Intersections . . . . . . . . . . . 7-207-15 AMFs Related to Geometric Design of Urban Unsignalized Intersections . . . . . . . . . . 7-237-16 Effect of Adding a Left-Turn Lane at an Urban Unsignalized Intersection . . . . . . . . . 7-237-17 AMFs for Excluding a Left-Turn Lane at an Urban Unsignalized Intersection . . . . . . 7-237-18 AMFs for Adding a Right-Turn Lane at an Urban Unsignalized Intersection . . . . . . . 7-247-19 AMFs for Number of Through Lanes at Urban Unsignalized Intersections . . . . . . . . . 7-247-20 Coefficient Analysis for Lane Width at Urban Unsignalized Intersections . . . . . . . . . 7-257-21 AMFs for Median Presence at Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . 7-277-22 Coefficient Analysis for Median Width at Urban Unsignalized Intersections . . . . . . . 7-27

Chapter 1 Introduction

Roadway Safety Design Synthesis 11/1/20051-1

Chapter 1Introduction

Page

OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

HIGHWAY SAFETY AND GEOMETRIC DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3Defining the Safety Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3Conscious Consideration of Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4Overview of Safety-Conscious Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

ROLE OF SAFETY-CONSCIOUS DESIGN IN THE TxDOT DESIGN PROCESS . . . 1-6

PURPOSE AND ORGANIZATION OF THE SYNTHESIS . . . . . . . . . . . . . . . . . . . . . . . . 1-9Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10



OVERVIEW

The traditional approach to highway geometric design incorporates a nominal level of safetythrough adherence to minimum design criteria for key design elements. The level of safety providedis referred to as “nominal” because the correlation between actual crash frequency and key designelements is unknown by the designer. Ideally, guidance relating design choices to crash frequency(and severity) would be available to help guide the engineer during the design process such that:

! Each design component provides an acceptable level of safety.! The design features that comprise the design are consistent in the degree of safety provided.! The combination of design components for each design feature is cost-effective (i.e., neither

over- nor under-designed).! The benefits derived from the resulting design can be shown to outweigh its costs and

represent the best use of limited program funds.

The objective of this document is to synthesize information in the literature thatquantitatively describes the relationship between various geometric design components and safety.This information is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in the Roadway Safety DesignWorkbook (1).

HIGHWAY SAFETY AND GEOMETRIC DESIGN

This part of the chapter describes the nature of the highway safety problem and the role ofgeometric design in providing a safe highway system. Initially, crash data are examined to quantifycurrent highway crash trends in Texas and the United States. Then, the need for a more explicitconsideration of safety in the design process is outlined. Finally, a process is described that can beused by designers to evaluate the impact of alternative design decisions on safety.

Defining the Safety Problem

During the past 40 years, the safe and efficient operation of the nation’s highways has beena growing public concern. High-speed freeways, changes in vehicle size and power, and anincreasingly mobile society led to serious safety problems and an increasing death toll on roads inthe United States. Fatal crash data cited in Traffic Safety Facts (2) indicate that 50,900 people diedin motor vehicle related crashes in 1966. The fatality rate that year was 5.5 fatalities per 100 millionvehicle-miles traveled (f/hmvm). By 1995, additional safety technology in vehicles and roadsideobjects, and improved design processes resulted in this rate being reduced to 1.73 f/hmvm (a69 percent reduction).

In 1995, the American Association of State Highway and Transportation Officials(AASHTO) undertook the development of a strategic highway safety plan. The plan was adoptedin December 1997 (3). The goal of the plan was to reduce fatalities by 5000 to 7000 per year by year2004 (i.e., to between 37,000 and 39,000 fatalities in 2004). The data in Table 1-1 provide anindication of progress toward this goal. As indicated by these data, the annual number of fatalities



has not changed; however, the amount of travel has increased by 13 percent. As a result, the fatalityrate has decreased from 1.73 to 1.52 f/hmvm (a 12 percent reduction). Nevertheless, further safetyimprovements will be needed nationally to reduce the annual number of fatalities and achieve theAASHTO goal.

Table 1-1. National Motor Vehicle Crash Statistics for 1995 and 2000.Category Statistics Year Change, %

1995 2000Crashes Total 6,699,000 6,394,000 -5

Fatal 37,200 37,400 1Fatalities Total 41,800 41,800 0

Collisions with pedestrians 5600 4700 -16Collisions with bicycles 800 700 -13Other 35,400 36,400 3

Exposure Vehicles registered 197,065,000 217,028,000 10Motor-vehicle-miles (millions) 2,423,000 2,750,000 13

Rates Fatal crashes per 100 million vehicle-miles 1.54 1.36 -11Fatalities per 100 million vehicle-miles 1.73 1.52 -12

Crash data from Texas were compared to similar data for the United States to gain insighton the nature of the highway safety problem within Texas. Summary statistics that facilitate thiscomparison are listed in Table 1-2. They are based on crash records for 2000. They indicate that3800 fatalities occurred on Texas highways that year, representing about 9 percent of the nation’s41,800 fatalities. When normalized by vehicle-miles of travel, Texas had a fatality rate of1.73 f/hmvm, which is about 14 percent higher than the national average. It was also noted thatpedestrian fatality rates in Texas are about 20 percent higher than the national average.

Conscious Consideration of Safety

In 1974, AASHTO defined a safe roadway as follows:

“A safe roadway is one in which none of the driver-vehicle-roadway interactionsapproaches the critical level at any point along its length.” (4)

Put another way, neither the physics of keeping a vehicle on the roadway nor the driver’s mentalworkload should approach their limits on a safe roadway. Roadway designers should keep this idealcondition in mind and provide for it wherever possible. Intuitively, a straight, flat roadway with fewat-grade access points is safer than a roadway with steep grades, sharp curves, and frequent accesspoints. However, few roadways can be constructed without some consideration for curvature, grade,and access. In practice, the roadway designer must consult guidelines, conduct analyses, and relyon judgment to determine the most acceptable curve radii and allowable grades.



Table 1-2. Comparison of Texas with National Motor Vehicle Crash Statistics.Category Statistics Year 2000 Difference,

%United States TexasCrashes Total 6,394,000 300,000

Fatal 37,400 3200Deaths Total 41,800 3800

Collisions with pedestrians 4700 412Collisions with bicycles 700 37Other 36,400 3351

Exposure Vehicles registered 217,028,000 14,300Motor-vehicle-miles (millions) 2,750,000 220,000Population (thousands) 274,600 20,100

Rates Fatal crashes per 100 million vehicle-miles 1.36 1.45 7Fatalities per 100 million vehicle-miles 1.52 1.73 14Pedestrian fatalities per 100,000 persons 1.71 2.05 20Bicycle fatalities per 100,000 persons 0.25 0.18 -28

Design guidelines often identify minimum acceptable design criteria that, if adhered to, areintended to provide a safe highway design. These criteria appear in various places, such asAASHTO’s A Policy on Geometric Design of Highways and Streets (5) and TxDOT’s RoadwayDesign Manual (6). Oftentimes, considerations of cost, safety, and efficiency have resulted innumerous elements of a roadway just satisfying the criteria. Subsequent experience with some ofthese roadways has revealed that more generous (and more forgiving) levels of design are associatedwith fewer crashes. Closer examination of the elements associated with minimum design oftenrevealed that their combination at specific locations on the roadway may accumulate to push driversand vehicles to their performance limits. In recognition of this realization, AASHTO commentedin 1974:

“...While minimum standards may have been adequate for the existing or even theassumed conditions, they may be inadequate if speeds and traffic volumes increasemore rapidly than anticipated...Frequently, a more liberal design would have costlittle more over the life of the project and would increase its safety and usefulnesssubstantially...Often the safety deficiencies generated by minimum design areimpossible to correct by any known device or appurtenance. A warning sign is apoor substitute for adequate geometric design...Highways built with high designstandards put the traveler in an environment which is fundamentally safer becauseit is likely to compensate for the driving errors he will eventually make.” (4)

AASHTO additionally recommended consistency in design and the use of above-minimumdesign element dimensions, especially in the areas of sight distance, right-of-way width, andsideslopes. This recommendation is intended to result in the use of more “forgiving” design



dimensions and thereby, produce a safer highway system. In more recent years, this idea has evolvedinto a process called Safety-Conscious Design.

Overview of Safety-Conscious Design

In recent years, the safety provided by the nation’s highway system has come under additionalscrutiny, not just for safety but increased security. The Transportation Equity Act for the 21st

Century (TEA-21) has required states to provide for consideration of projects and strategies that willincrease the safety and security of the transportation system for motorized and non-motorized users.To achieve further large reductions in crash frequency, research indicates that it will be necessaryto change the focus of future safety initiatives from driver behavior to design policies andtechnologies that reduce the likelihood of a crash, just as AASHTO recommended in 1974. Theconscious consideration of safety in the design processes is one way to accomplish this goal.

Safety-conscious design represents the explicit evaluation of the safety consequencesassociated with design alternatives. It is incorporated at key points in the design process wherechanges necessary to accommodate safety considerations can be easily incorporated. This processcan be contrasted with the traditional design process where minimum design criteria are used toconstrain design element combinations and sizes with the implicit assumption that the resultingdesign will provide an acceptable level of safety.

The concept of “safety-conscious design” was first described in Special Report 214 (7).More recently, the Transportation Association of Canada (TAC) incorporated safety-consciousdesign in its design guide for new location and reconstruction projects (i.e., the Geometric DesignGuide for Canadian Roads) (8). The justification offered for changing its design philosophy wasthe observation that: (1) the traditional approach to design has become less dependent on experienceand judgment and more dependent on adherence to minimum criteria; (2) there is a belief amongdesigners that safety is an automatic by-product of the design process; and (3) the difficultiesassociated with quantifying safety have relegated safety considerations to being only a secondaryobjective of the design process.

Safety-conscious design can be implemented by using safety evaluation tools to quantify theeffect of alternative design choices on safety. These tools, combined with economic principles, areused to evaluate the benefits and costs of design alternatives. In recognition of the time requiredto use these tools, the evaluations tend to be reserved for more complex design conditions or thosethat involve high construction costs.

ROLE OF SAFETY-CONSCIOUS DESIGN IN THE TxDOT DESIGN PROCESS

This part of the chapter provides an overview of TxDOT’s design process and illustrateswhere safety-conscious design concepts are applied (or can be introduced). This process is part ofa larger project development process that takes the project from concept to letting. This processconsists of six stages: planning and programming; preliminary design; environmental; right-of-wayand utilities; plans, specifications, and estimates (PS&E) development; and letting. The planningand programming, preliminary design, and PS&E development stages are stages where safety can



Direction, Rules-of-Thumb

Design Criteria

Warrants, etc.

Design Guides

Preliminary Design

PS&EDevelop-

ment

Safety (crashes)

Evaluation Tools

Operations (delay)

Cost ($)

Planning & Programming

Application Criteria

Guidelines

be explicitly considered in the design process. The sequence of these stages in the developmentprocess is shown in Figure 1-1.

Figure 1-1. Components of the Project Development Process.

As indicated by Figure 1-1, evaluation tools are used by the designer to verify theperformance potential of alternative designs. The evaluation quantifies the design’s performancein terms of safety, operations, construction cost, etc. The objective of this evaluation is to ensure thatthe design offers a reasonable balance between cost and effectiveness. Tools are readily availableto conduct level-of-service analyses and to estimate construction costs. Tools for quantifying analternative’s impact on safety are not as readily available at this time.

There are two stages of the project development process that embody the design process.These stages are: (1) preliminary design and (2) PS&E development. During the preliminary designstage, the location of a facility (if it is new or being relocated) and its major design features areidentified. Then, alternative locations and features are considered and the more promising ones areevaluated in greater detail.

The final design of the proposed facility is undertaken during the PS&E development stage.The environmental and right-of-way issues have generally been resolved by the start of this stage anda “preferred” alignment has been identified. The main product of this stage is a completed plan setwith appropriate specifications for construction. Another product of this stage is a list of estimatedmaterial quantities needed for the construction bidding process.

Table 1-3 identifies safety tasks that can be undertaken in TxDOT’s project developmentprocess (9). Also identified is the step in the corresponding development process stage within whichthey would be conducted.

As indicated in Table 1-3, “key” design elements are identified in Step 4 of the preliminarydesign stage and then used to direct the safety evaluation tasks. Key design elements are thoseelements that: (1) are associated with the “controlling criteria” that dictate the need for a designexception or have a known effect on safety, and (2) are used in situations where atypical conditionsexist, the design is complex, or construction costs are high. The controlling criteria vary by projecttype (6); those applicable to Rehabilitation Projects (3R) include:



! Design Speed ! Lane Width! Shoulder Width ! Bridge Width! Structural Capacity ! Horizontal Alignment! Vertical Alignment ! Grade! Stopping Sight Distance

Table 1-3. Potential Safety Tasks in the Project Development Process.Stage Step Potential Safety-Related Task

Planning andprogramming

1. Needs identification • Screen facilities for locations with safety needs.

Preliminarydesign

1. Preliminary design conference • Document safety needs.• Identify atypical conditions, complex elements, and

high-cost components.2. Data collection/preliminary design

preparation• Diagnose safety data to identify crash patterns.• Refine project scope if necessary.

4. Preliminary schematic • Perform preliminary level of safety analysis for“key” design elements.1

5. Geometric schematic • Perform detailed level of safety analysis for “key”design elements.1

6. Value engineering • Compare cost of specific elements and overallroadway with safety and operational benefits.

7. Geometric schematic approval • Document safety of design choices (use results fordesign exception request, if necessary).

PS&Edevelopment

3. Final alignments/profiles • Re-evaluate alignment, cross section, and roadsidedesign to ensure acceptable level of safety.

9. Traffic control plan • Evaluate safety of long-term detour roadway design.Note:1 - Key design elements are those elements that: (1) are associated with the controlling criteria specified for the project

or have a known effect on safety, and (2) are used in situations where atypical conditions exist, the design iscomplex, or construction costs are high.

The controlling criteria for New Location and Reconstruction Projects (4R) include all of theabove criteria plus: cross slope, superelevation, and vertical clearance. Additional important designelements that may also be considered as “key” because of their known effect on safety include: turnbays at intersections, median treatment, and clear zone (i.e., horizontal clearance). For non-keydesign elements, the traditional design process (i.e., compliance with design criteria and warrants)will likely provide an acceptable level of safety.

The implementation of these tasks will add time to the design process. However, by limitingthe evaluation of safety to primarily “key” design elements, it is hoped that the additional timerequired will be kept to a minimum and incurred only where it is likely to provide some return interms of improved safety, lower construction cost, or both. This added time represents an immediateand direct cost to the design process. However, it also represents a more cost-effective approach todesign because additional benefit will be derived through fewer crashes (by provision of effectivefeatures) and lower construction costs (by not over-designing some design elements).



PURPOSE AND ORGANIZATION OF THE SYNTHESIS

Purpose

The purpose of the Roadway Safety Design Synthesis is to present a compilation of theavailable, quantitative safety information for roadway design. Qualitative (i.e., non-numeric) safetyinformation is available from other sources, notably the AASHTO Highway Safety Design andOperations Guide (10). The safety information presented in this synthesis allows the roadwaydesigner to have a deeper understanding of the sources, ranges, and limitations of the quantitativeinformation contained in the Roadway Safety Design Workbook (1).

Organization

The Roadway Safety Design Synthesis is divided into seven chapters. The first chapterintroduces the Synthesis. The subsequent six chapters synthesize the available quantitativeinformation for various roadway facilities. These “quantitative” chapters are titled:

! Freeways,! Rural Highways,! Urban Streets,! Interchange Ramps,! Rural Intersections, and! Urban Intersections.

Each chapter contains two main parts. The first part describes safety prediction models thatpredict the expected number of crashes that will occur on a particular roadway segment, interchangeramp, or intersection. These models are compared and discussed, providing a roadway designersome insight into the model types and design-related factors that correlated with crash frequency.The safety performance models in each chapter were used to generate the crash rates shown in thecorresponding chapter of the Roadway Safety Design Workbook (1).

The second part of each chapter contains accident modification factors (AMFs) for variousdesign-related factors that have been found to be correlated with crash frequency. AMFs representthe relative change that occurs in crash frequency when a particular geometric component is added,removed, or changed in size. As such, it is multiplied by the expected crash frequency before thechange to estimate the expected crash frequency after the change. An AMF in excess of 1.0 is anindication that the corresponding change will increase crash frequency. An AMF less than 1.0indicates that the change will decrease crash frequency.

Differences in crash reporting threshold among agencies can introduce uncertainty in crashdata analysis and regional comparison of crash trends. A majority of the crashes that often gounreported (or, if reported, not filed by the agency) are those identified as “property-damage-only.”In contrast, severe crashes (i.e., those crashes with an injury or fatality) tend to be more consistentlyreported across jurisdictions. Thus, safety relationships tend to be more transferrable amongjurisdictions when they are developed using only severe crash data. In recognition of this benefit,this document is focused on models and AMFs applicable to severe crashes. Unless explicitly statedotherwise, all references to “crash frequency” refer to severe crash frequency.



There is frequent reference in this document to the traffic “lane” or “lanes” provided in theroadway or at an intersection. All such references pertain to the through traffic lane or lanes, unlessexplicitly stated otherwise. Lanes for turning traffic are referenced in terms of the turn maneuverthey serve (e.g., two-way left-turn lane, right-turn lane, etc.).

The AMFs and crash rates in this document are derived from research conducted throughoutthe United States, including Texas. All of the research findings were screened for applicability toTexas conditions. Several AMFs require the distribution of crashes (by crash type or median type)as an input. The distributions tabulated herein for these AMFs were obtained from the crashdatabase maintained by the State of Texas, Department of Public Safety (DPS).

The AMFs described in this document were neither compared to DPS crash data to confirmthe stated trends, nor calibrated to Texas conditions. As a general rule, AMFs are not the subject ofsuch examinations on a local level due to the high cost of the effort and the limitations of local data.Moreover, experience indicates that AMFs derived from large, multi-state databases tend to providethe accuracy needed for the comparative assessment of design alternatives for any given location.

REFERENCES

1. Roadway Safety Design Workbook. Texas Transportation Institute, The Texas A&M UniversitySystem, College Station, Texas, 2005.

2. Traffic Safety Facts 2000: A Compilation of Motor Vehicle Crash Data from the FatalityAnalysis Reporting System and the General Estimates System. National Highway Traffic SafetyAdministration, National Center for Statistics and Analysis, U.S. Department of Transportation,Washington, D.C., December 2001.

3. AASHTO Strategic Highway Safety Plan. American Association of State Highway andTransportation Officials, Washington, D.C., 1998.

4. Highway Design and Operational Practices Related to Highway Safety, 2nd ed. AmericanAssociation of State Highway and Transportation Officials, Washington, D.C., 1974.

5. A Policy on Geometric Design of Highways and Streets. American Association of State Highwayand Transportation Officials, Washington, D.C., 2004.

6. Roadway Design Manual. Texas Department of Transportation, Austin, Texas, October 2002.

7. Special Report 214 - Designing Safer Roads: Practices for Resurfacing, Restoration, andRehabilitation. Transportation Research Board, Washington, D.C., 1987.

8. Geometric Design Guide for Canadian Roads. Part 1 and Part 2. Transportation Associationof Canada, Ottawa, Canada, 1999.

9. Project Development Process Manual. Texas Department of Transportation, Austin, Texas,August 2003.

10. Highway Safety Design and Operations Guide. American Association of State Highway andTransportation Officials, Washington, D.C., 1997.

Chapter 2 Freeways


Chapter 2Freeways

Page

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4

SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4Hadi Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5Persaud and Dzbik Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7Wang Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7Comparison of Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10

Horizontal Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11Vertical Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13

Lane Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13Outside Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15Inside Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17Median Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18Shoulder Rumble Strips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20

Roadside Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21Appurtenances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22

Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25

Chapter 2 Freeways


INTRODUCTION

A freeway is intended to provide mobility to travelers, with minimal interference fromentering or exiting traffic. It has a divided, multilane cross section that reflects a “generous” designcondition (i.e., design element sizes consistently exceed minium design criteria). The freeway isgrade-separated whenever it intersects another route such that freeway movements flow freely,without interruption by traffic control devices. Freeways require considerable amounts of right-of-way. The cost of this right-of-way, especially in urban areas, presents challenges to the developmentof freeway designs that are not only safe and efficient but also cost-effective.

The development of a safe, efficient, and economical freeway design typically reflects theconsideration of a variety of design alternatives, especially when access to the freeway is included.A variety of techniques exist for estimating the operational benefits of alternatives; many areautomated through software tools. Techniques for estimating construction and right-of-way costsare also available to the designer. Unfortunately, techniques for estimating the safety benefits ofalternative designs are not as readily available. This chapter summarizes information in the literaturethat can be used to estimate the crash frequency associated with various freeway design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various freeway design components and safety. This informationis intended to provide a basis for the development of a procedure for estimating the safety benefitof alternative designs. This procedure is documented in Chapter 2 of the Roadway Safety DesignWorkbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical freeway segment. They include variables for traffic volume and segmentlength. They also include variables for other factors considered to be correlated with crash frequency(e.g., median type, number of lanes, etc.). One or more AMFs can be multiplied by the expectedcrash frequency obtained from the prediction model to produce an estimate of the expected crashfrequency for a specific freeway segment.

Scope

This chapter addresses the safety of the main lanes of a freeway segment. It does not addressthe safety of interchange ramps, ramp gores, and frontage roads. For this reason, the crashesaddressed herein are referred to as “mid-junction” crashes. Crashes that occur at, or are related to,ramps and frontage roads are the subject of Chapter 5.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a widevariation in reporting threshold among cities and states. This variation complicates the extrapolationof crash trends found in one location to another location. Moreover, it can confound the

Chapter 2 Freeways


development of safety prediction models using data from multiple agencies. Reporting thresholdis strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given roadway will below if it is located in an area with a high reporting threshold. In contrast, this same roadway willhave a high crash frequency if it is located in an area with a low reporting threshold. This problemis minimized when crash data analyses, comparisons, and models are based on data pertaining onlyto severe crashes.

Overview

This chapter documents a review of the literature related to freeway safety. The focus is onquantitative information that relates severe crash frequency to various geometric design componentsof the freeway main lanes. The review is not intended to be comprehensive in the context ofreferencing all works that discuss freeway safety. Rather, the information presented herein is judgedto be the most current information that is relevant to freeway design in Texas. It is also judged tobe the most reliable based on a review of the statistical analysis techniques used and the explanationof trends.

Where appropriate, the safety relationships reported in the literature are compared herein,with some interpretation offered to explain any differences noted. The relationships are typicallypresented as reported in the literature; however, the names or the units of some variables have beenchanged to facilitate their uniform presentation in this chapter.

This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various freeway design components and severe crashfrequency. As previously noted, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 2 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels reported in the literature are described. In the second part, accident modification factors aredescribed. Within this part, the various factors examined are organized into the following categories:roadway geometric design, roadside design, and “other” factors.

SAFETY PREDICTION MODELS

Described in this part of the chapter are several models that were developed to estimate theexpected frequency of crashes on freeway segments. Four of the five models were specificallydeveloped for freeway segments. The fifth model was developed for rural divided highways, whichare similar to rural freeways except for the provision of access from intersecting roadways. Afterthe models are summarized, they are then compared graphically for a range of common inputconditions.

Chapter 2 Freeways


CUF,4 ' 0.25 ADT 1.1832 (1000 L)0.7733 e BUF,4 (2-3)

CRF ' 0.25 ADT 0.9599 (1000 L)0.9107 e BRF (2-1)

BRF ' &14.032 & 0.0407 Wis % 0.2127 Nx (2-2)

BUF,4 ' &10.61 & 0.307 Wl & 0.0232 Ws & 0.0154 V % 0.24 Nx & 0.06 (Wm)0.5 (2-4)

Hadi Models

The models described in this section are derived from the equations reported by Hadi et al.(2). They used negative binomial regression analysis to calibrate a set of safety prediction modelsusing data from Florida roadways. The models are categorized by crash severity, area type (i.e.,urban, rural), and number of through lanes. The three freeway models developed by Hadi et al.address the following facility types:

! rural freeways with four or six lanes, ! urban four-lane freeways, and! urban six-lane freeways.

These models are listed below as Equations 2-1, 2-3, and 2-5, respectively.

with,

where:CRF = frequency of mid-junction injury crashes on rural freeways, crashes/yr;

ADT = average daily traffic, veh/d;L = freeway segment length, mi;

Wis = inside shoulder width, ft; andNx = number of interchanges on freeway segment.

with,

where:CUF,4 = frequency of mid-junction injury crashes on urban four-lane freeways, crashes/yr;

Wl = lane width, ft;Ws = outside shoulder width, ft;V = speed limit, mph; and

Wm = median width, ft.

Chapter 2 Freeways


with,

where:CUF,6 = frequency of mid-junction injury crashes on urban six-lane freeways, crashes/yr.

The models developed by Hadi et al. (2) estimate injury crash frequency only; they do notinclude PDO or fatal crash frequency. Hadi et al. prepared separate models for estimating total crashfrequency and fatal crash frequency. Analysis of these models indicates that the estimates obtainedfrom Equations 2-1, 2-3, and 2-5 should be inflated by 5 percent (i.e., multiplied by 1.05) to obtainan estimate of severe crash frequency.

The sign of the constant associated with any single variable in the model’s linear terms (i.e.,those variables in Equations 2-2, 2-4, and 2-6) indicates the correlation between a change in thevariable value and injury crash frequency. For example, the negative sign of the constant associatedwith speed limit V in Equation 2-4 indicates that injury crash frequency is lower on roads with ahigher speed limit. This trend is likely a reflection of the fact that higher speed roads are typicallybuilt to have more generous design element sizes and more forgiving roadside safety features. It mayalso be possible that drivers are more cautious when driving at higher speeds.

The characteristics of the data used by Hadi et al. (2) are summarized in Table 2-1. Theyused four years of crash data to develop their safety prediction models. They did not report thenumber of road segments reflected in the database. However, the road segments used were on theFlorida state highway system.

Table 2-1. Database Characteristics for Various Freeway Safety Prediction Models.Model Developers Database Characteristics

Area Type Years ofCrash Data

Number ofRoad Segments

Total SectionLength, mi

Number ofThrough Lanes

Hadi et al. (2) Rural 4 not available not available 4, 6Urban 4 not available not available 4Urban 4 not available not available 6

Persaud & Dzbik (3) Urban 2 not available 991 4Urban 2 not available 247 More than 4

Wang et al. (4) Rural 6 622 432 3, 4

CUF,6 ' 0.25ADT 1.405L 0.93 e BUF,6 (2-5)

BUF,6 ' &14.04 & 0.339 Wl & 0.0594 Ws & 0.031 (Wm)0.5 (2-6)

Chapter 2 Freeways


CUF,6 ' 0.0000099 ADT 1.206 L (2-8)

BRH ' 0.131 Rhaz & 0.151 Iac % 0.034 Dd % 0.163 Dit % 0.052 Dwo& 0.572 Ifc & 0.094 Ws & 0.003 Wm % 0.429 Iat

' 0.131 (1) & 0.151 (1) % 0.034 (0) % 0.163 (0) % 0.052 (0)& 0.572 (1) & 0.094 Ws & 0.003 Wm % 0.429 (0)

' &0.592 & 0.094 Ws & 0.003 Wm

(2-10)

CUF,4 ' 0.0000354 ADT 1.082 L (2-7)

CRH ' 0.000233 ADT 1.073 L 1.073 e BRH (1 & 0.01 PDO) (2-9)

Persaud and Dzbik Models

Persaud and Dzbik (3) developed two prediction models using data for urban freeways inOntario, Canada. Separate models were developed for total crashes and severe (fatal plus injury)crashes. The models for severe crashes are presented in Equations 2-7 and 2-8.

Unlike the models by Hadi et al. (2), the models by Persaud and Dzbik do not includevariables for specific roadway elements (e.g., lane width, posted speed limit, median width, etc.).Moreover, the freeway segments do not distinguish between those with and those without rampspeed-change lanes. Because speed-change lanes tend to be associated with more crashes than basicfreeway segments, the model predictions may overestimate crash frequency for mid-junctionsegments.

The characteristics of the data used by Persaud and Dzbik (3) are summarized in Table 2-1.They used two years of crash data to develop their safety prediction models. They reported that theyused approximately 500 freeway “sections” in their database. However, they did not provide abreakdown of the number of segments that had four lanes and the number that had more than fourlanes.

Wang Model

Wang et al. (4) developed a safety prediction model for rural multilane divided highwaysusing crash and geometry data from Minnesota. The database does not include data for freeways.However, the behavior of a rural divided highway with few or no access points is similar to that ofa rural freeway. Equations 2-9 and 2-10 describe this model.

with,

Chapter 2 Freeways


where:CRH = frequency of severe mid-junction crashes on rural multilane highways, crashes/yr;Rhaz = roadside hazard rating (1, 2, ..., 7; where 1 represents best and 7 is worst from a safety

standpoint);Iac = access control (1 for partial control, 0 for no control);Dd = driveway density, driveways/mi;Dit = density of unsignalized intersections with turn lanes, intersections/mi;

Dwo = density of unsignalized intersections without turn lanes, intersections/mi;Ifc = functional class (1 for rural principal arterial, 0 otherwise);

Ws = outside shoulder width, ft; Iat = area location type (1 for highways in a rural municipality, 0 otherwise); and

PDO = percent property-damage-only crashes on rural multilane divided highways (= 62.5).

As indicated in Equation 2-10, the model contains some variables that are not relevant tofreeway applications, such as driveway density and intersection density. Values for these variablesthat are appropriate for freeways (e.g., driveway density of 0 driveways/mi) were substituted in theoriginal model to obtain a reduced model form suitable for freeway-like highway segments. Theroadside hazard rating describes the relative safety of the roadside. A rating of “1” is assigned toroadsides with horizontal clearances of 30 ft or more and side slopes of 1V:4H or flatter.

Equation 2-9 was originally derived to predict total crashes (i.e., PDO plus injury and fatal).An adjustment multiplier of “1 !0.01 PDO” was added to this equation to convert the predictioninto severe crash frequency. This term requires an estimate of the percentage of PDO crashes. Thispercentage is estimated at 62.5 percent for rural multilane divided highways in Minnesota (5).

The characteristics of the data used by Wang et al. (4) are summarized in Table 2-1. Theyused five years of crash data for 622 multilane highway segments to develop their safety predictionmodels.

Comparison of Crash Models

The crash prediction models described in the previous sections are compared in this section.The objective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. The values of other model variables were set at typical values forfreeways. These values are listed in Table 2-2.

Chapter 2 Freeways


0

5

10

15

20

25

30

0 50 100 150 200

Average Daily Traffic Demand (1000's), veh/d

Seve

re C

rash

Fre

quen

cy,

cra

shes

/yr

1.0-mile segment length

Urban, 6-Lane (Persaud & Dzbik [3])

Urban, 6-Lane (Hadi et al. [2])

Urban, 4-Lane (Persaud & Dzbik [3])Urban, 4-Lane (Hadi et al. [2])

Table 2-2. Typical Values Used for Freeway Model Comparison.Model Variable Typical

ValueSafety Prediction Model Developer

Hadi et al. (2) Persaud &Dzbik (3)

Wang et al.(4)

Rural UrbanFour Lane

Urban Six Lane

UrbanFour & Six

Rural Four Lane

Inside shoulder width, ft 4 U -- -- -- --Outside paved shoulder width, ft 10 -- U U -- U

Lane width, ft 12 -- U U -- --Median width, ft 30 -- U U -- U

Speed limit, mph 55 -- U -- -- --Interchanges per mile 0 U U -- -- --

The expected severe crash frequencies obtained from the various models are shown inFigures 2-1 and 2-2. The model developer and facility type for a given trend line is indicated in eachfigure. Several trends can be seen in these figures. First, the trends indicate that severe crashfrequency increases in a nearly linear manner with traffic volume. However, crash frequency onurban six-lane freeways increases more rapidly than the crash frequency on urban four-lane freeways.Second, comparing across the two figures, it appears that rural four-lane freeways have fewer crashesthan their urban counterparts.

Figure 2-1. Severe Crash Frequency for Urban Freeways.

Chapter 2 Freeways


0

1

2

3

4

0 10 20 30 40 50 60


Sev

ere

Cra

sh F

requ

ency

, c

rash

es/y

r

1.0-mile segment length

Rural (Hadi et al. [2])

Rural (Wang et al. [4])

Figure 2-2. Severe Crash Frequency for Rural Freeways.

ACCIDENT MODIFICATION FACTORS

This part of the chapter describes various accident modification factors that are related to thedesign of an urban or rural freeway. The various factors examined are organized into the followingcategories: roadway geometric design, roadside design, and “other” factors.

Geometric Design

This section describes AMFs related to the geometric design of a freeway. Topicsspecifically addressed are listed in Table 2-3. Many geometric design components or elements arenot listed in Table 2-3 (e.g., weaving section length) that are also likely to have some effect on severecrash frequency. However, a review of the literature did not reveal useful quantitative informationdescribing these effects. The list of available AMFs for freeway geometric design is likely toincrease as new research in this area is undertaken.

Table 2-3. AMFs Related to Geometric Design of Freeways.Section Accident Modification Factor

Horizontal alignment Horizontal curve radiusVertical alignment GradeCross section Lane width Outside shoulder width Inside shoulder width

Median width Shoulder rumble strips

In some instances, an AMF is derived from a safety prediction model as the ratio of “segmentcrash frequency with a changed condition” to “segment crash frequency without the change.” In

Chapter 2 Freeways


AMFcr '

1.55 Lc %80.2

R& 0.012 Is

1.55 Lc

(2-11)

AMFcr ' 1 %1Ic

5590R

2

(2-12)

other instances, the AMF is obtained from a before-after study. Occasionally, crash data reportedin the literature were used to derive an AMF.

All of the AMFs described in this section are developed to yield a value of 1.0 when theassociated design component or element represents a “typical” condition. Deviation from this basecondition to a more generous or desirable design condition results in an AMF of less than 1.0.Deviation to a more restricted condition results in an AMF of more than 1.0.

Horizontal Alignment

This subsection describes AMFs related to horizontal alignment. However, no reliable AMFsspecific to freeway alignments were found during the literature review. The only horizontalalignment AMF found in the literature is for horizontal curve radius. This section summarizes thisreview of the literature.

Zegeer et al. (6) developed a model for determining the safety of horizontal curves on two-lane rural highways. This model was subsequently modified by Harwood et al. (7) to produce ahorizontal curve AMF. The equation for this AMF is:

where:AMFcr = horizontal curve accident modification factor;

Lc = length of horizontal curve (= Ic × R / 5280 / 57.3), mi;Ic = curve deflection angle, degrees;R = curve radius, ft; and Is = presence of a spiral transition curve (1 if a spiral transition is present, 0 otherwise).

While not developed for freeway segments, this AMF is widely recognized as a reliable reflectionof the relationship between curvature and crash frequency on two-lane highways.

Raff (8) examined curve and tangent crash rates for four-lane, controlled access highways.A regression analysis of these rates (described in Chapter 3) revealed the following relationshipbetween curve radius and crash rate CR: CR = 1.20 + (6130/R)2 × 1/Ic (R2 = 0.96). The AMFderived from this relationship is:

Figure 2-3 compares the two AMFs for a range of curve radii and deflection angles. Thetrend lines indicate that the AMF converges to 1.0 as the curve radius increases for both two-laneundivided and four-lane divided highways. For a given radius, larger deflection angles correspondto lower AMF values. This trend suggests that most curve crashes are associated with the curveentry maneuver such that curves with a larger deflection angle (for a given radius) are easier for the

Chapter 2 Freeways


AMFg ' (e b Pg & 1.0)Ps % 1.0 (2-13)

1.0

1.2

1.4

1.6

1.8

2.0

800 1200 1600 2000 2400 2800

Curve Radius, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Def. Angle = 10 deg.

30 deg.30 deg.

Harwood et al. (7)Derived from Raff (8)

10 deg.

driver to detect in advance and safely negotiate the entry maneuver. In spite of these basicsimilarities, the trend lines shown suggest that divided, controlled-access highways have greatersensitivity (in terms of increased crash risk) to curvature than two-lane highways. Given the age ofthe Raff data and the fact that the controlled-access highways were not explicitly stated to befreeways, an accurate AMF for freeway horizontal curvature cannot be derived from these data.

Figure 2-3. Horizontal Curve AMF for Freeways.

Vertical Alignment

This subsection describes AMFs related to features of the freeway’s vertical alignment. Atthis time, the only AMF addressed in this subsection is grade.

The relationship between grade and crash frequency was derived from the safety predictionmodel developed by Milton and Mannering (9). This AMF is based on a mix of urban and ruralmultilane highways in Washington State. The highways were classified as principal arterials. Theyhave up to six lanes and ADTs of up to 18,000 veh/d per lane. This AMF is shown in Figure 2-4.

Also shown in Figure 2-4 is an AMF developed by Harwood et al. (7). It is based on ruraltwo-lane highway crash data. They presented it in tabular form (i.e., AMF values are offered forspecific grades); however, a best-fit trend line is shown in the figure. Although not derived fromfreeway crash data, the Harwood AMF provides some validation of the Milton and Mannering AMF.

The Harwood AMF and the Milton and Mannering AMF can be described using Equation 2-13. The base condition for grade is 0 percent (i.e., flat). That is, flat freeway segments have a gradeAMF equal to 1.0. The grade variable is an absolute value implying that the AMF has the samevalue, regardless of whether the grade is uphill or downhill.

Chapter 2 Freeways


0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8

Grade, %

Acc

iden

t Mod

ifica

tion

Fact

or

Urban & Rural Principal Arterials(Milton & Mannering [9])

Rural 2-Lane Highways(Harwood et al. [7])

where:AMFg = grade accident modification factor;

b = regression coefficient;Pg = percent grade (absolute value), %; andPs = proportion of crashes to which the AMF applies.

Figure 2-4. Grade AMF for Freeways.

The values of variables b and Ps in Equation 2-13 are provided in Table 2-4. For example,substitution of the values of 0.019 and 1.0 for b and Ps, respectively, results in the trend line shownin Figure 2-4 that is attributed to Milton and Mannering (9).

Table 2-4. Coefficient Values for Grade on Freeways.Model Source Roadway Type Crash

SeveritySubset of

Influenced Crash TypesSubset

Proportion, PsCoefficient

bMilton &Mannering (9)

Urban & rural principalarterials

All All 1.0 0.019

Harwood et al. (7) Rural, 2-lane, undivided All All 1.0 0.016

The trend lines shown in Figure 2-4 indicate that the AMF for grade ranges from 1.0 for0 percent to 1.14 for 8 percent. Based on this analysis, the Milton and Mannering AMF is reasonedto be applicable to urban and rural freeways.

Cross Section

Lane Width. A relationship between lane width and crash frequency was derived from thesafety prediction models developed by several researchers. This derivation is described in the

Chapter 2 Freeways


AMFi ' (AMFb & 1.0)Pi

Pb

% 1.0 (2-15)

AMFlw,b ' e &0.047 (Wl & 12) (2-14)

AMFlw, i ' (e &0.047 (Wl & 12)& 1.0)

Pi

0.37% 1.0 (2-16)

Geometric Design section of Chapter 3. When applied to freeways, the following equation wasdeveloped for computing the lane width AMF for the base combination of lanes and median type(i.e., rural, four-lane freeway). The base condition lane width for this AMF is 12 ft.

where:AMFlw, b = lane width accident modification factor for the base combination of lanes and median

type (i.e., rural, four-lane freeway).

Equation 2-14 can be combined with the following equation to obtain the lane width AMFfor other combinations of lanes and median type.

where:AMFi = adjusted accident modification factor for lane and median combination i; AMFb = accident modification factor for base combination of lanes and median type;

Pi = proportion of “related” crashes that occur on roadways with lane and median combinationi; and

Pb = proportion of “related” crashes that occur on roadways with the base combination of lanesand median type.

The values of Pi and Pb correspond to the crashes influenced by the AMF, and are both representedas a proportion of all crashes. The crash distribution used for Pi is that reflecting the crash historyof the roadway type corresponding to bi. The distribution used for Pb is that reflecting a specifiedbase combination of lanes and median type. For this analysis, a rural, four-lane freeway was chosento represent the base combination. The proportion of influential crashes for the base combinationPb is 0.37.

The AMF that results from the combination of Equations 2-14 and 2-15 is:

It can be tailored to a desired number of lanes and median type by using the variable Pi. Values forthis variable are listed in Table 2-5. The proportions in this table (and subsequent similar tables)were obtained from the crash database maintained by the Texas Department of Public Safety.

The AMF obtained from Equation 2-16 is illustrated in Figure 2-5. It is labeled “derived”and has a bold line weight. It is compared to the AMFs developed by two other researchers (seeTable 3-7, Chapter 3). The trend is one of increasing AMF value with a reduction in lane width.The AMFs attributed to Hadi et al. (2) suggest that a 1 ft reduction in lane width results in a 35 to40 percent increase in crashes. This increase is unrealistically large and is probably a result ofcolinearity among variables in the safety prediction model developed by Hadi et al.

In Figure 2-5, the AMF attributed to Harwood et al. (10) was developed for divided highways(instead of freeways) by an expert panel convened by Harwood. It is shown in the figure because

Chapter 2 Freeways


AMFswo,b ' e &0.021 (Ws & 10) (2-17)

0.8

1.0

1.2

1.4

1.6

1.8

10 10.5 11 11.5 12

Lane Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 4-Lane, FreewayUrban, 6-Lane, Freeway(Hadi et al. [2])

Rural, 4-Lane, Divided Highway(Harwood et al. [10])

Rural & Urban, 4-Lane, Freeway (derived)

it is in general agreement with the AMF computed using Equation 2-16 and offers evidence of biasin the two AMFs attributed to Hadi et al (2). It is rationalized that the design and operationaldifferences between a freeway and a divided highway (as related solely to the correlation betweenlane width and crash frequency) are not so distinct as to invalidate this comparison.

Table 2-5. Crash Distribution for Freeway Lane Width AMF.Facility Type Area Type Crash Type Subset Through Lanes Subset Proportion

Freeway Rural Single-vehicle run-off-road, same direction sideswipe

4 0.376 0.49

Urban Single-vehicle run-off-road,same direction sideswipe

4 0.406 0.408 0.40

10 0.43

Figure 2-5. Lane Width AMF for Freeways.

Outside Shoulder Width. The following equation represents the shoulder width AMF forthe base combination of lanes and median type (i.e., rural, four-lane freeway). It was derived in asimilar manner as the lane width AMF. The base condition shoulder width is 10 ft.

where:AMFswo, b = outside shoulder width accident modification factor for the base combination of lanes

and median type (i.e., rural, four-lane freeway); andWs = outside shoulder width, ft.

Chapter 2 Freeways


AMFswo, i ' ( e &0.021 (Ws & 10)& 1.0)

Pi

0.15% 1.0 (2-18)

0.8

1.0

1.2

1.4

1.6

1.8

6 7 8 9 10 11 12

Outside Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 6-Lane, Freeway (Hadi et al. [2])

Multilane Highway (Knuiman et al. [11])

Urban & Rural, 4- & 6-Lane Freeway (derived)

Equation 2-17 can be combined with Equation 2-15 to obtain the outside shoulder widthAMF for other combinations of lanes and median type. The proportion of influential crashes for thebase combination Pb is 0.15. The resulting AMF is:

It can be tailored to the desired number of lanes and median type by using the variable Pi. The valueof this variable is selected from Table 2-6.

Table 2-6. Crash Distribution for Freeway Outside Shoulder Width AMF.Area Type Crash Type Subset Through Lanes Subset Proportion

Rural Single-vehicle run-off-road, right side 4 0.156 0.19

Urban Single-vehicle run-off-road, right side 4 0.166 0.148 0.1210 0.13

The AMF obtained from Equation 2-18 is illustrated in Figure 2-6. It is labeled “derived”and has a bold line weight. It is compared to the AMFs developed by other researchers. The trendis one of increasing AMF value with a reduction in shoulder width. The AMFs attributed to Hadi etal. (2) and Knuiman et al. (11) are believed to be overly sensitive to shoulder width due to colinearityamong the variables in their respective regression models.

Figure 2-6. Outside Shoulder Width AMF for Freeways.

Chapter 2 Freeways


AMFswi, i ' ( e &0.021 (Wis & Wsb )& 1.0)

Pi

0.15% 1.0 (2-19)

A shoulder width AMF was derived from the model developed by Wang et al. (4). However,it was very sensitive to shoulder width. In fact, it has a value of 2.5 when the shoulder width is0.0 ft, which is much higher than the values obtained from other AMFs. An examination of the dataevaluated by Wang et al. indicated that only 4 percent of the segments had shoulder widths less than4 ft, yet these same segments accounted for 20 percent of the crashes. Hence, it is likely that thereare unspecified factors that underlie this over-representation of crashes when categorized by shoulderwidth. For these reasons, the AMF derived from the Wang model was not considered further.

Inside Shoulder Width. A review of the literature revealed only one safety predictionmodel that included a variable for inside shoulder of a freeway. It was developed by Hadi et al. (2).However, when the regression coefficient associated with the inside-shoulder-width variable in thismodel was compared with coefficients for outside shoulder width (see Chapter 3), no significantdifference was found between coefficients. Hence, Equation 2-17 is rationalized to be equallyapplicable to inside shoulder width. It was combined with Equation 2-15 to obtain the followinginside shoulder width AMF:

where:AMFswi = inside shoulder width accident modification factor;

Wis = inside shoulder width, ft; andWsb = base inside shoulder width (= 4.0 ft for four lanes and 10.0 ft for six or more lanes).

The base condition for this AMF is a 4 ft inside shoulder width for four-lane freeways and a 10 ftwidth for freeways with six or more lanes. The proportion of influential crashes for the basecombination Pb is 0.15. Equation 2-19 can be tailored to the desired number of lanes and mediantype by using the variable Pi. The value of this variable is selected from Table 2-7.

Table 2-7. Crash Distribution for Freeway Inside Shoulder Width AMF. Area Type Crash Type Subset Through Lanes Subset Proportion

Rural Single-vehicle run-off-road, left side 4 0.156 0.20

Urban Single-vehicle run-off-road, left side 4 0.156 0.138 0.1210 0.11

The AMF obtained from Equation 2-19 for a four-lane rural freeway is illustrated in Figure 2-7. It is labeled “derived” and has a bold line weight. It is compared to the AMF developed by Hadiet al. (2). The trend is one of increasing AMF value with a reduction in shoulder width. The HadiAMF is believed to be overly sensitive to shoulder width due to colinearity among the variables intheir respective regression models. A weighted regression analysis was used to negate some of thisbias. Details of this analysis are described in the Geometric Design section of Chapter 3.

Chapter 2 Freeways


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 100

Median Width, ft

Rel

ativ

e Ef

fect

on

Inju

ry C

rash

es

Illinois Data

Utah Data

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10

Inside Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

orRural Freeway(derived)

Rural Freeway (Hadi et al. [2])

Figure 2-7. Inside Shoulder Width AMF for Freeways.

Median Width. An AMF for median width was developed from safety prediction modelsdeveloped by Hadi et al. (2) and from data reported by Knuiman et al. (11). The Hadi AMF is basedon models developed for four-lane and six-lane urban freeways. Knuiman et al. examined crashdata for rural freeways, urban freeways, and major highways. The crash rate adjustment factors(analogous to AMFs) they computed are shown in Figure 2-8, as are the “best-fit” trend lines.

Figure 2-8. Relationship between Median Width and Severe Crash Frequency.

Equation 2-20 was developed to represent the AMFs derived from the literature. The basecondition for this AMF is a median width of 76 ft for depressed medians and 24 ft for surfaced (i.e.,flush-paved) medians. The coefficients used in this equation are listed in columns 4 through 6 ofTable 2-8.

Chapter 2 Freeways


AMFmw 'b0 (e b1 W

b2m & 1.0) % 1.0

b0 (e b1 Wb2

mb & 1.0) % 1.0(2-20)

0.6

0.8

1.0

1.2

1.4

1.6

10 15 20 25 30 35 40

Median Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

4-Lane (Hadi et al.[2])Utah, 4-Lane (Knuiman et al.[11])

Derived

Illinois, 4-Lane (Knuiman et al.[11])

where:AMFmw = median width accident modification factor;

Wmb = base median width (24 ft for surfaced median; 76 ft for depressed median), ft; andWm = median width, ft.

Table 2-8. Coefficient Values for Median Width on Freeways.Model Source Roadway Type Crash

SeverityBase Coefficients Equivalent b1

Coeff.b0 b1 b2 Wm< 40ft Wm> 40ft

Hadi et al. (2) Urban, 4-lane, freeway Injury 1.0 -0.060 0.5 -0.060 -0.060Urban, 6-lane, freeway Injury 1.0 -0.037 0.5 -0.037 -0.037

Knuiman et al.(11)

Urban & rural, 4-lane, freeway (Utah) Severe 0.488 -0.00111 2.0 -0.153 -0.055Urban & rural, 4-lane, freeway (Illinois) Severe 0.483 -0.00020 2.0 -0.042 -0.111

Weighted Average: -0.046 -0.050

Figure 2-9 illustrates the AMFs listed in Table 2-8 for four-lane freeways. They have a basecondition median width of 24 ft. Similar trends are obtained for a base width of 76 ft. Two of theAMFs are in good agreement. The AMF from Knuiman et al. using Utah data is less in agreementand indicates a greater sensitivity to median width for widths of 40 ft or less.

Figure 2-9. Median Width AMF for Freeways.

The derived AMF relationship is shown in Figure 2-9. It is based on Equation 2-20 with b0= 1.0, b2 = 0.5, and the weighted average of the equivalent b1 coefficients listed in columns 7 and 8

Chapter 2 Freeways


AMFrs ' (0.88 & 1.0) Pi % 1.0 (2-21)

of Table 2-8 (where the weight w for each coefficient is equal to its reciprocal squared [i.e., w =1/b2]). The equivalent b1 coefficient for each model source was derived from a regression analysisusing Equation 2-20 with b0 = 1.0 and b2 = 0.5 for median widths ranging from 10 to 40 ft. Theanalysis was repeated for median widths ranging from 40 to 80 ft. The AMFs obtained fromEquation 2-20 (using the base coefficients) served as the dependent variable.

Shoulder Rumble Strips. Griffith (12) investigated the correlation between the presenceof continuous, rolled-in rumble strips and crash frequency on urban and rural freeways in Californiaand Illinois. The focus of his examination was single-vehicle run-off-road crashes. The reportedcrash data were used to calculate a rumble strip AMF. These calculations are shown in Table 2-9.

Table 2-9. AMFs for Shoulder Rumble Strips on Freeways.Data

SourceState Crash

SeverityTreated Site Crashes 1 Comparison Site Crashes Base

AMF (frs)2StandardDeviation3

After Before After BeforeGriffith

(12)Illinois All 1895 2801 1833 2288 0.84 0.036California All 469 579 364 417 0.93 0.088Combined All 2364 3380 2197 2705 0.86 0.034Illinois Injury 877 1135 765 874 0.88 0.059

Notes:1 - Analysis applies to single-vehicle run-off-road crashes.2 - frs = Aftertreated × Beforecomp / (Beforetreated × Aftercomp).3 - Standard deviation = frs × (1/Aftertreated + 1/Beforecomp + 1/Beforetreated + 1/Aftercomp)0.5.

The shoulder rumble strip AMF can be computed using Equation 2-21. It is based on theoverall base AMF for severe crashes in Table 2-9. For Texas applications, it requires the appropriatecrash distribution proportion for the roadway type of interest. These proportions are listed inTable 2-10.

where:AMFrs = shoulder rumble strip accident modification factor; and

Pi = proportion of influential crashes that occur on roadway type i (from Table 2-10).

Table 2-10. Crash Distribution for Freeway Shoulder Rumble Strip AMF.Area Type Crash Type Subset Through Lanes Subset Proportion

Rural Single-vehicle run-off-road, either side 4 0.306 0.39

Urban Single-vehicle run-off-road, either side 4 0.316 0.278 0.2410 0.25

Chapter 2 Freeways


AMFpd ' (fp & 1.0) Ps % 1.0 (2-22)

Roadside Design

This section describes AMFs related to the roadside design of a freeway segment. Topicsspecifically addressed are listed in Table 2-11. Many roadside design components or elements thatare not listed in this table (e.g., ditch shape) are also likely to have some correlation with severe crashfrequency on the freeway segment. However, a review of the literature did not reveal that their effecthas been quantified by previous research. The list of available AMFs for freeway roadside designis likely to increase as new research in this area is undertaken.

Table 2-11. AMFs Related to Roadside Design of Freeways.Section Accident Modification Factor

Cross section Utility pole densityAppurtenances see text

AMFs for roadside safety appurtenances are not described in this chapter because theygenerally do not exist. The safety literature related to roadside appurtenances has focused on theinformation needed to evaluate the cost-effectiveness of installing individual appurtenances atspecific locations. The information is very detailed due to the design and operational complexity ofvarious appurtenances and the influence of site-specific conditions on their performance. Moreover,safety appurtenances may sometimes increase crash frequency while, more importantly, reducingthe severity of the crash. For these reasons, the safety benefits derived from an appurtenance aretypically estimated on an individual, case-by-case basis using the techniques described in theRoadside Design Guide (13).

Cross Section

This subsection is devoted to the presentation of AMFs related to the roadside cross sectionof a freeway. A review of the literature indicates that horizontal clearance, side slope, utility poleoffset, and bridge width may have some influence on crash frequency. However, these correlationshave not been quantified for freeways. Rather, the focus of previous research has been on rural, two-lane highways. The one exception is utility pole offset. This research included crashes on urban andrural divided highways in the database. This subsection describes an AMF for utility pole offset and“density” (where pole density relates to pole frequency per unit length of roadway).

The relationship between utility pole offset, pole density, and crash frequency was evaluatedby Zegeer and Parker (14). They developed a safety prediction model using data from four states.The model included average pole offset, traffic volume, and pole density as independent variables.The AMF derived from this model is described in Equation 2-22. Details of the model are describedin Table 2-12. The base condition is 25 poles/mi and a pole offset of 30 ft.

with,

Chapter 2 Freeways


fp '(0.0000984 ADT % 0.0354 Dp ) W &0.6

o & 0.040.0000128 ADT % 0.075

(2-23)

where:AMFpd = utility pole accident modification factor;

Dp = utility pole density (two-way total), poles/mi; andWo = average pole offset from nearest edge of traveled way, ft.

Table 2-12. Coefficient Values for Utility Pole Density along Freeways.Model Source Roadway Type Crash

SeveritySubset of


Proportion, PsZegeer & Parker (14) Urban and rural roads All Single-vehicle collision with pole 0.022

The subset proportions appropriate for Texas freeway applications are provided inTable 2-13. Equation 2-22 yields an AMF that ranges from 1.08 at a pole density of 50 poles/mi andoffset of 10 ft to 0.99 at a pole density of 10 poles/mi and offset of 30 ft. The AMF is more sensitiveto pole offset than it is to density or average daily traffic volume.

Table 2-13. Crash Distribution for Freeway Utility Pole Density AMF.Area Type Crash Type Subset Through Lanes Subset Proportion

Rural Single-vehicle collision with pole 4 0.0306 0.038

Urban Single-vehicle collision with pole 4 0.0466 0.0298 0.01610 0.012

Appurtenances

As discussed previously, AMFs for roadside safety appurtenances are not described in thischapter. The safety literature related to roadside appurtenances has focused on the informationneeded to evaluate the cost-effectiveness of installing individual appurtenances at specific locations.Most of the research conducted in this area has been incorporated into a comprehensive procedurefor evaluating appurtenances on a case-by-case basis. This procedure is outlined in a report by Makand Sicking (15) and automated in the Roadside Safety Analysis Program (RSAP) (16).

RSAP can be used to evaluate alternative roadside safety appurtenances on individual roadsegments. The program accepts as input information about the road segment geometry and trafficcharacteristics. It also allows the analyst to describe the roadside cross section, location of fixedobjects, and safety appurtenance design. Table 2-14 summarizes the various RSAP inputs. The

Chapter 2 Freeways


AMFsl ' e b (V & 55) (2-24)

output from RSAP includes an estimate of annual crash frequency as well as the road-user costsassociated with these crashes. The crash reduction potential realized by adding a roadside safetyappurtenance (or changing the roadside cross section) can be estimated by specifying the changedcondition as an “alternative.”

Table 2-14. RSAP Input Data Requirements.Design

CategoryDesign Component Design Element

General -- Area type (urban/rural) Functional classOne-way/two-way Speed limitSegment length

Trafficcharacteristics

-- Traffic volume (ADT) Truck percentageTraffic growth factor

Geometricdesign

Horizontal alignment Direction of curve RadiusVertical alignment GradeCross section Divided/undivided Number of lanes

Lane width Shoulder widthMedian type Median width

Roadsidedesign

Cross section Foreslope BackslopeParallel ditches Intersecting slopes

Fixed object Offset Side of roadwayType (wood pole, headwall, etc.) SpacingWidth

Safety appurtenances Offset Side of roadwayType (barrier, cushion, etc.) Flare rateLength Width

Other Adjustment Factors

This section describes AMFs related to features of the freeway that are not categorized asrelated to geometric design or roadside design. At this time, the only AMF addressed in this sectionis speed limit.

Two safety prediction models developed for freeways in urban and rural settings were foundto have a variable for speed limit. One of these models was developed by Hadi et al. (2). Anotherwas that developed by Milton and Mannering (9). A generalized AMF form is shown inEquation 2-24 for a base speed limit of 55 mph. It can be used to represent the AMF obtained fromboth of the two prediction models by proper substitution of the coefficient b from Table 2-15.

where:AMFsl = speed limit accident modification factor; and

V = speed limit, mph.

Chapter 2 Freeways


0.6

0.8

1.0

1.2

1.4

1.6

40 45 50 55 60 65 70

Speed Limit, mph

Acc

iden

t Mod

ifica

tion

Fact

or

Urban & Rural Freeways (derived)

Urban, 4-Lane, Freeway(Hadi et al. [2])


The two AMFs are compared in Figure 2-10. The two coefficients reported by Milton andMannering are so similar that they plot as one trend line. The trends in the figure indicate that higherspeed limits are associated with fewer severe crashes. Although not shown in the figure, similartrends have been found in safety prediction models developed for urban streets. It is likely that anincrease in speed limit does not make the freeway safer; rather, it probably indicates that freewayswith a higher speed limit tend to have a more generous design.

Table 2-15. Coefficient Values for Speed Limit on Freeways.Model Source Roadway Type Crash

SeveritySubset of Influenced

Crash TypesCoefficient

bHadi et al. (2) Urban, 4-lane, freeway Injury All -0.0154Milton & Mannering (9) Urban & rural, principal arterials All All -0.0111 1

-0.0103 Weighted Average: -0.012

Note:1 - Separate safety prediction models were developed for data from principal arterials in the eastern and western half

of Washington State.

Figure 2-10. Speed Limit AMF for Freeways.

The derived AMF relationship is shown in Figure 2-10. It uses the weighted average of theb coefficients listed in Table 2-15 (where the weight w for each coefficient is equal to its reciprocalsquared [i.e., w = 1/b2]). There is insufficient data to determine if this coefficient varies by number-of-lanes or area type. Hence, the derived AMF is offered as approximate for all lanes and area typesuntil new information becomes available.

Chapter 2 Freeways


REFERENCES


2. Hadi, M.A., J. Aruldhas, L-F. Chow, and J.A. Wattleworth. “Estimating Safety Effects of Cross-Section Design for Various Highway Types Using Negative Binomial Regression.”Transportation Research Record 1500. Transportation Research Board, Washington, D.C.,1995, pp. 169-177.

3. Persaud, B., and L. Dzbik. “Accident Prediction Models for Freeways.” TransportationResearch Record 1401. Transportation Research Board, Washington, D.C., 1993, pp. 55-60.

4. Wang, J., W.E. Hughes, and R. Stewart. Safety Effects of Cross-section Design for Rural, Four-Lane, Non-Freeway Highways. Report No. FHWA-RD-98-071. Federal HighwayAdministration, Washington, D.C., May 1998.

5. Zegeer, C., H. Huang, J. Stewart, R. Pfefer, and J. Wang. “Effects of a Towaway ReportingThreshold on Crash Analysis Results.” Transportation Research Record 1635. TransportationResearch Board, Washington, D.C., 1998, pp. 49-57.

6. Zegeer, C.V., R. Stewart, D. Reinfurt, F.M. Council, T. Neuman, E. Hamilton, T. Miller, and W.Hunter. Cost-Effective Geometric Improvements for Safety Upgrading of Horizontal Curves.Report No. FHWA-RD-90-021. Federal Highway Administration, Washington, D.C., 1990.

7. Harwood, D.W., F.M. Council, E. Hauer, W.E. Hughes, and A. Vogt. Prediction of the ExpectedSafety Performance of Rural Two-Lane Highways. Report No. FHWA-RD-99-207. FederalHighway Administration, Washington, D.C., 2000.

8. Raff, M. “Interstate Highway-Accident Study.” Highway Research Board Bulletin 74. HighwayResearch Board, Washington, D.C., 1953.

9. Milton, J., and F. Mannering. The Relationship between Highway Geometrics, Traffic RelatedElements, and Motor Vehicle Accidents. Report No. WA-RD 403.1. Washington StateTransportation Center, University of Washington, Seattle, Washington, March 1996.

10. Harwood, D.W., E.R. Kohlman Rabbani, K.R. Richard, H.W. McGee, and G.L. Gittings.NCHRP Report 486: Systemwide Impact of Safety and Traffic Operations Design Decisions for3R Projects. Transportation Research Board, Washington, D.C., 2003.

11. Knuiman, M.W., F.M. Council, and D.W. Reinfurt. “Association of Median Width andHighway Accident Rates.” Transportation Research Record 1401. Transportation ResearchBoard, Washington, D.C., 1993, pp. 70-82.

Chapter 2 Freeways


12. Griffith, M.S. “Safety Evaluation of Rolled-In Continuous Shoulder Rumble Strips Installed onFreeways.” Transportation Research Record 1665. Transportation Research Board, Washington,D.C., 1999, pp. 28-34.

13. Roadside Design Guide. 3rd Edition. American Association of State Highway andTransportation Officials, Washington, D.C., 2002.

14. Zegeer, C.V., and M.R. Parker. Cost-Effectiveness of Countermeasures for Utility PoleAccidents. Report No. FHWA-RD-83-063. Federal Highway Administration, Washington,D.C., September 1983.

15. Mak, K., and D.L. Sicking. NCHRP Report 492: Roadside Safety Analysis Program (RSAP) -Engineer’s Manual. Transportation Research Board, Washington, D.C., 2003.

16. Mak, K., and D.L. Sicking. Roadside Safety Analysis Program (RSAP) - User’s Manual.NCHRP Project 22-9. National Cooperative Highway Research Program, Washington, D.C.,June 2002.

Chapter 3 Rural Highways


Chapter 3Rural Highways

Page


SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4Rural Two-Lane Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5

Hadi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5Vogt and Bared Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

Rural Multilane Highways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7Hadi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7Wang Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8

Comparison of Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9

Horizontal Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Horizontal Curve Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Spiral Transition Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13

Vertical Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15

Lane Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15Outside Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20Inside Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22Median Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22Shoulder Rumble Strips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24Centerline Rumble Strip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-25TWLTL Median Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26Superelevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-27Passing Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-27

Roadside Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-28Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-28

Horizontal Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-28Side Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-29Utility Pole Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-29Bridge Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-30

Appurtenances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-32Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36



INTRODUCTION

Rural highways provide a high speed network of roadways that serve traffic movementsbetween urban areas. Between densely populated metropolitan areas, these highways often have adivided, multilane cross section. Highways serving smaller towns or shorter trip lengths typicallyhave lower volume and a two-lane undivided cross section. About one-third of the vehicle miles oftravel in the state of Texas occur on rural highways, yet these highways are associated with aboutone-half of all fatal crashes. In general, crashes on rural highways tend to be more severe than thoseon urban streets, due largely to the higher speeds associated with rural highways. For these reasons,efforts to accommodate “desirable” design elements in rural highway design, and to provide aforgiving roadside, are often cost-effective.

The development of a safe, efficient, and economical rural highway design typically reflectsthe consideration of a variety of design alternatives. A variety of techniques exist for estimating theoperational benefits of alternatives; many are automated through software tools. Techniques forestimating construction and right-of-way costs are also available to the designer. Unfortunately,techniques for estimating the safety benefits of alternative designs are not as readily available. Thischapter summarizes information in the literature that can be used to estimate the crash frequencyassociated with various highway design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various rural highway design components and safety. Thisinformation is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in Chapter 3 of the RoadwaySafety Design Workbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical highway segment. They include variables for traffic volume and segmentlength. They also include variables for other factors considered to be correlated with crash frequency(e.g., median type, number of lanes, etc.). One or more AMFs can be multiplied by the expectedcrash frequency obtained from the prediction model to produce an estimate of the expected crashfrequency for a specific highway segment.

Scope

This chapter addresses the safety of rural highway segments. It does not address the safetyof intersections on these highways. For this reason, the crashes addressed herein are referred to as“mid-block” crashes. Crashes that occur at, or are related to, rural intersections are the subject ofChapter 6.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a wide



variation in reporting threshold among cities and states. This variation complicates the extrapolationof crash trends found in one location to another location. Moreover, it can confound thedevelopment of safety prediction models using data from multiple agencies. Reporting thresholdis strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given roadway will below if it is located in an area with a high reporting threshold. In contrast, this same roadway willhave a high crash frequency if it is located in an area with a low reporting threshold. This problemis minimized when crash data analyses, comparisons, and models are based on data pertaining onlyto severe crashes.

Overview

This chapter documents a review of the literature related to rural highway safety. The focusis on quantitative information that relates severe crash frequency to various geometric designcomponents of the highway. The review is not intended to be comprehensive in the context ofreferencing all works that discuss rural highway safety. Rather, the information presented herein isjudged to be the most current information that is relevant to highway design in Texas. It is alsojudged to be the most reliable based on a review of the statistical analysis techniques used and theexplanation of trends.


This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various highway design components and severe crashfrequency. As previously noted, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 3 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels reported in the literature are described. In the next part, accident modification factors aredescribed. Within this part, the various factors examined are organized into the following categories:roadway geometric design, roadside design, and “other” factors.


Described in this part of the chapter are several models that were developed to estimate theexpected frequency of crashes on rural highway segments. Two of the models described werespecifically developed for rural two-lane highway segments. Two other models were developed formultilane highway segments. After the models are summarized, they are then compared graphicallyfor a range of common input conditions.



Rural Two-Lane Highways

This section addresses safety prediction models for rural two-lane highways. Two sets ofmodels are described and are identified by the names of their developers. They include:

! Hadi Model! Vogt and Bared Model

Hadi Model

The model described in this subsection is derived from the equations reported by Hadi et al.(2). They used regression analysis to calibrate a set of safety prediction models using data fromFlorida roadways. The models are categorized by crash severity, area type (i.e., urban, rural), andnumber of through lanes. The rural two-lane highway model developed by Hadi et al. is:

with,

where:C = frequency of mid-block injury crashes on rural two-lane highways, crashes/yr;

ADT = average daily traffic, veh/d;L = highway segment length, mi;

Wl = lane width, ft;V = speed limit, mph;Ni = number of intersections on highway segment; andWs = shoulder width (paved or unpaved), ft.

The models developed by Hadi et al. (2) estimate injury crash frequency only; they do notinclude PDO or fatal crash frequency. Hadi et al. prepared separate models for estimating total crashfrequency and fatal crash frequency. Analysis of these models indicates that the estimates obtainedfrom Equation 3-1 should be inflated by 5 percent (i.e., multiplied by 1.05) to obtain an estimate ofsevere crash frequency.

The sign of the constant associated with any single variable in the model’s linear terms (i.e.,those variables in Equation 3-2) indicates the correlation between a change in the variable value andinjury crash frequency. For example, the negative sign of the constant associated with speed limitV suggests that injury crash frequency is lower on roads with a higher speed limit. In this case, thetrend is an aberration of the modeling approach because injuries are generally recognized to increasewith speed. The trend is likely a reflection of the fact that higher speed roads are typically built tohave more generous design element sizes and more forgiving roadside safety features. Hence, thespeed limit constant is acting as a surrogate for several unspecified design elements and features.

C ' 0.001547 ADT 0.868 L 0.8157 e B1 (3-1)

B1 ' &0.0787 Wl & 0.0108 V % 0.0601 Ni & 0.021 × 2 Ws (3-2)




Table 3-1. Database Characteristics for Rural Two-Lane Highway Safety Prediction Models.Model Developers Database Characteristics

Data Source Years of CrashData

Number of RoadSegments


Hadi et al. (2) Florida DOT 4 not available not availableVogt & Bared (3) Minnesota DOT 5 619 706

Washington DOT 3 712 534

Vogt and Bared Model

Vogt and Bared (3) investigated the relationships between crash frequency and various ruralhighway geometry and operational attributes. They developed a safety prediction model forpredicting the frequency of severe crashes on rural two-lane highways. The form of this model is:

with,

where:C = frequency of severe crashes on two-lane highways, crashes/yr;

Rhaz = roadside hazard rating (1, 2, ..., 7; where 1 represents best and 7 is worst from a safetystandpoint);

Dd = driveway density, driveways/mi;Dr = weighted average degree of curvature, degrees/ft;Vr = weighted average vertical curvature, %/ft; and

IWash = indicator variable for location of segment (1 for Washington State, 0 for Minnesota).

The characteristics of the data used by Vogt and Bared (3) are summarized in Table 3-1. Thedatabase they used to develop the safety prediction model represents five years of crash data for 619highway segments in Minnesota and three years of data for 712 segments in Washington State.

C ' 0.0005197 ADT L e B1 % B2 (3-3)

B1 ' &0.1306 Wl & 0.0784 Ws % 0.0598 Rhaz % 0.0062 Dd (3-4)

B2 ' 0.0457 Dr % 0.4694 Vr % 0.4309 IWash (3-5)



Rural Multilane Highways

This section addresses safety prediction models for rural multilane divided highways. Twosets of models are described and are identified by the names of their developers. They include:

! Hadi Model! Wang Model

Hadi Model

The model described in this subsection is developed from the equations reported by Hadi etal. (2). They used regression analysis to calibrate a set of safety prediction models using data fromFlorida roadways. The models are categorized by crash severity, area type (i.e., urban, rural), andnumber of through lanes. The four-lane divided highway model developed by Hadi et al. is:

where:C = frequency of mid-block injury crashes on four-lane divided highways, crashes/yr.

The models developed by Hadi et al. (2) estimate injury crash frequency only; they do notinclude PDO or fatal crash frequency. Hadi et al. prepared separate models for estimating total crashfrequency and fatal crash frequency. Analysis of these models indicates that the estimates obtainedfrom Equation 3-1 should be inflated by 5 percent (i.e., multiplied by 1.05) to obtain an estimate ofsevere crash frequency.


Table 3-2. Database Characteristics for Rural Multilane Highway Safety Prediction Models.Model

DevelopersDatabase Characteristics

Data Source Years of CrashData

Number ofRoad Segments



Hadi et al. (2) Florida DOT 4 not available not available 4Wang et al. (4) Minnesota DOT 5 622 432 3, 4

C ' 0.000956 ADT 0.6919 L 0.6288 e 0.1973 Ni (3-6)



BRH ' 0.131 Rhaz & 0.151 Iac % 0.034 Dd % 0.163 Dit % 0.052 Dwo& 0.572 Ifc & 0.094 Ws & 0.003 Wm % 0.429 Iat

(3-8)

Wang Model

Wang et al. (4) developed a safety prediction model for rural multilane divided highwaysusing crash and geometry data from Minnesota. Equations 3-7 and 3-8 describe this model.

with,

where:CRH = frequency of severe mid-ramp crashes on rural highways, crashes/yr;Rhaz = roadside hazard rating (1, 2, ..., 7; where 1 represents best and 7 is worst from a safety

standpoint);Iac = access control (1 for partial control, 0 for no control);Dd = driveway density, driveways/mi;Dit = density of unsignalized intersections with turn lanes, intersections/mi;

Dwo = density of unsignalized intersections without turn lanes, intersections/mi;Ifc = functional class (1 for rural principal arterial, 0 otherwise);

Ws = outside shoulder width, ft; Iat = area location type (1 for highways in a rural municipality, 0 otherwise); and

PDO = percent property-damage-only crashes on rural multilane divided highways (= 62.5).

As indicated in Equation 3-8, the model contains a variable describing the relative degree ofhazard associated with the roadside. Specifically, a roadside hazard rating is used to describe thesafety of the highway cross section. A rating of “1” is assigned to roadsides with horizontalclearances of 30 ft or more and side slopes of 1V:4H or flatter.

Equation 3-7 was originally derived to predict total crashes (i.e., PDO plus injury and fatal).An adjustment multiplier of “1 !0.01 PDO” was added to this equation to convert the predictioninto severe crash frequency. This term requires an estimate of the percentage of PDO crashes. Thispercentage is estimated at 62.5 percent for rural multilane divided highways in Minnesota (5).

The characteristics of the data used by Wang et al. (4) are summarized in Table 3-2. Theirmodel is based on five years of crash data for 622 multilane highway segments.


The crash prediction models described in the previous sections are compared in this section.The objective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. The values of other model variables were set at typical values forrural highways. These values are listed in Table 3-3.

CRH ' 0.000233 ADT 1.073 L 1.073 e BRH (1 & 0.01 PDO) (3-7)



Table 3-3. Typical Values Used for Rural Highway Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

Hadi et al. (2) Vogt &Bared (3)

Wang et al.(4)

Two Lane Four Lane Two Lane Four LaneOutside shoulder width, ft 8 U -- U U

Median width, ft 40 -- -- -- --Lane width, ft 12 U -- U --Speed limit, mph 55 U -- -- --Roadside hazard rating 3 -- -- U U

Intersections per mile 0 U U -- U

Driveway density, driveways/mi 5 -- -- U U

Average degree of curvature 0.0 -- -- U --Average vertical curvature 0.0 -- -- U --Access control no control -- -- -- U

Functional class principal arterial -- -- -- U

Area location type non-municipal -- -- -- U

The expected severe crash frequencies obtained from the various models are shown inFigures 3-1 and 3-2. The model developer and facility type for a given trend line is indicated in eachfigure. The trend lines in these figures indicate that severe crash frequency increases in a nearlylinear manner with traffic volume. In fact, the crash frequency on multilane highways increases atabout the same rate as the crash frequency on two-lane highways.


This part of the chapter describes various accident modification factors that are related to thedesign of a rural highway. The various factors examined are organized into the following categories:roadway geometric design, roadside design, and “other” factors.

Geometric Design

This section describes AMFs related to the geometric design of a rural highway. Topicsspecifically addressed are listed in Table 3-4. Many geometric design components or elements arenot listed in Table 3-4 (e.g., pavement cross slope) that are also likely to have some effect on severecrash frequency. However, a review of the literature did not reveal useful quantitative informationdescribing these effects. The list of available AMFs for rural highway geometric design is likely toincrease as new research in this area is undertaken.

In some instances, an AMF is derived from a safety prediction model as the ratio of “segmentcrash frequency with a changed condition” to “segment crash frequency without the change.” Inother instances, the AMF is obtained from a before-after study. Occasionally, crash data reportedin the literature were used to derive an AMF.



0.0

0.4

0.8

1.2

1.6

2.0

0 5 10 15 20 25


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Rural Divided Highway1.0-mile segment length

Wang et al. (4)

Hadi et al. (2)

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10


Sev

ere

Cra

sh F

requ

ency

, cr

ashe

s/yr

Rural Two-Lane Highway1.0-mile segment length

Vogt & Bared (3)

Hadi et al. (2)

Figure 3-1. Severe Crash Frequency for Rural Two-Lane Highways.

Figure 3-2. Severe Crash Frequency for Rural Multilane Divided Highways.

Table 3-4. AMFs Related to Geometric Design of Rural Highways.Section Accident Modification Factor

Horizontal alignment Horizontal curve radius Spiral transition curveVertical alignment GradeCross section Lane width Outside shoulder width Inside shoulder width

Median width Shoulder rumble strips Centerline rumble stripTWLTL median type 1 Superelevation Passing lanes

Note:1 - TWLTL: two-way left-turn lane.



1.0

1.2

1.4

1.6

1.8

2.0

500 900 1300 1700 2100 2500 2900

Curve Radius, ft

Acc

iden

t Mod

ifica

tion

Fact

or

2-Lane, Undivided,Def. Angle = 20 deg.

30 deg.

40 deg.

Harwood et al. (7)Derived from Raff (8)

2-Lane, Undivided Def. Angle = 20 deg.

AMFcr '

1.55 Lc %80.2

R& 0.012 Is

1.55 Lc

(3-9)

1.0

1.2

1.4

1.6

1.8

2.0

500 900 1300 1700 2100 2500 2900

Curve Radius, ft

Acc

iden

t Mod

ifica

tion

Fact

or

2-Lane, Undivided

4-Lane, Controlled-Access

4-Lane, Divided

4-Lane, Undivided

Derived from Raff (8)Def. Angle = 20 deg.



Horizontal Curve Radius. Zegeer et al. (6) developed a model for determining the safetyof horizontal curves on rural two-lane highways. This model was subsequently modified byHarwood et al. (7) to produce a horizontal curve AMF. This AMF is shown in Equation 3-9.

where:AMFcr = horizontal curve accident modification factor;

Lc = length of horizontal curve (= Ic × R / 5280 / 57.3), mi;Ic = curve deflection angle, degrees;R = curve radius, ft; and Is = presence of a spiral transition curve (1 if a spiral transition is present, 0 otherwise).

The AMF computed using Equation 3-9 is shown in Figure 3-3a (using a solid trend line) fora typical range of two-lane highway curve radii and deflection angles. The trend lines indicate thatthe AMF converges to 1.0 as the curve radius increases. For a given radius, larger deflection anglescorrespond to lower AMF values. This trend suggests that most curve crashes are associated withthe curve entry maneuver such that curves with a larger deflection angle (for a given radius) areeasier for the driver to detect in advance and safely negotiate the entry maneuver.

a. Two-Lane Highways. b. Multilane Highways.

Figure 3-3. Horizontal Curve AMF for Rural Highways.



CR ' b0 %b 2

1

Ic R 2 (3-10)

AMFcr ' 1 %1Ic

c0

R

2

(3-11)

The numerator of Equation 3-9, when multiplied by the volume of vehicles per year (inmillions), can be used to estimate the total number of annual crashes on a horizontal curve on a two-lane highway, as developed by Zegeer et al. (6). Their model also included an adjustment factor fortotal roadway width (i.e., shoulder plus lane width). The model suggested by the numerator ofEquation 3-9 is applicable to roads with a typical, total width of 30 ft. Thus, the constant “1.55”represents the crash rate CR (in crashes/million-vehicle-miles [crashes/mvm]) for a tangent sectionof highway. More generally, for curves without spiral transitions, this model can also be written as:

where b0 equals 1.55 and b1 equals 4930.

Equation 3-10 can be converted to the following generalized AMF form by dividing bothsides of the equation by the tangent crash rate term b0:

where c0 = b1 ×b0 -0.5.

Raff (8) examined curve crash rates for multilane and two-lane highways. He computedrates for four radius categories for each facility type. These rates are listed in Table 3-5.

The average curve deflection angles for each radius category were not reported by Raff (8).To compensate for this deficiency, geometric data for 29 rural, two-lane highway curves in six stateswere available from a report by Bonneson (9) to examine this relationship. An analysis of these datarevealed the following relationship: Ic = 11.3 (5730/R)0.590. The coefficient of determination R2 forthis relationship is 0.50. This relationship was checked against curve data reported by Milton andMannering (10) for rural minor arterials in eastern Washington State and found to yield very goodagreement. However, its extrapolation to data reported for rural principal arterials in WashingtonState (i.e., multilane, divided highways) indicated that it overestimated the average deflection angleby 54 percent. Thus, the previous relationship was adjusted to yield the following equation fordivided highways: Ic = 7.30 (5730/R)0.590. The deflection angle estimated for each radius using theseequations is listed in Table 3-5.

Weighted linear regression was used with Equation 3-10 to quantify the relationship betweencrash rate and curve radius for the data in Table 3-5. The weight used for each radius category wasthe reported number of crashes associated with that category. The results of the analysis are reportedin the last four columns of Table 3-5. Listed in the last row of the table are the regression constantsthat yield the equivalent of Equation 3-9. The resulting AMFs are shown in Figure 3-3b for a 20-degree deflection angle. The two-lane, undivided highway AMF obtained from the Raff (8) data andthe Harwood et al. (7) AMF are compared in Figure 3-3a for a common, 20-degree deflection angle.



AMFcr ' 1 %1Ic

5800R

2

(3-12)

Table 3-5. Crash Rate Analysis for Various Rural Highway Cross Sections.Road Type(Reference)

Variable Radius, ft 1 Statistics3820 1270 716 477 bo b1 co R2

Two-lanehighway (8)

Deflection angle, deg 14.4 27.4 38.5 49.0 1.76 4530 3410 0.99Crash rate, crashes/mvm 1.6 2.5 2.8 3.5

Crashes 504 596 338 354Four-lane,undividedhighway (8)


Crashes 98 90 16 3Four-lane,dividedhighway (8)


Crashes 95 65 5 12Four-lane,controlled-access (8)

Deflection angle, deg 9.3 17.7 24.9 -- 1.20 6130 5590 0.96Crash rate, crashes/mvm 1.6 2.3 4.5 --

Crashes 180 162 38 --Two-lanehighway (7)

-- -- -- -- -- 1.55 4930 3960 --

Note:1 - Radii listed represent the midpoint value for each radius category reported by Raff (8).

The comparison in Figure 3-3a suggests that the Raff AMF is in general agreement with theHarwood AMF. Differences between the two AMFs may be due to the use of estimated deflectionangles. The trends in Figure 3-3b indicate that the four-lane, undivided roadway may have a slightlylower AMF value than the two-lane highway trend; however, the difference is small and may beattributable to differences in deflection angle present in Raff’s database. A similar claim can bemade when comparing the AMFs for divided and controlled-access highways. However, the largeincrease in AMF value for these two highway types, beyond that for the two-lane, undividedhighway, cannot be explained by error in estimating the deflection angles.

Based on this analysis, the AMF developed by Harwood et al. (7) (i.e., Equation 3-9) isrationalized to be applicable to two-lane and four-lane, undivided highways. In contrast, thefollowing AMF should be used for four-lane, divided highways:

where, the “5800” constant was computed by multiplying the constant c0 of 4980 by the ratio of thec0 constants for two-lane highways (i.e., 5800 = 4980 × 3960 / 3410). This adjustment is intendedto maintain, in Equations 3-9 and 3-12, the relationship between the two-lane, undivided and four-lane, divided highways that is found in the Raff data.

Spiral Transition Curve. Equation 3-9 was used to derive an equation relating two-lanehighway crash frequency and the presence of a spiral transition curve. The form of this equation is:



AMFsp '

1.55 Lc %80.2

R& 0.012

1.55 Lc %80.2

R

(3-13)

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8

Grade, %

Acc

iden

t Mod

ifica

tion

Fact

or


Rural, 2-Lane Highways(Harwood et al. [7])

where:AMFsp = spiral transition curve accident modification factor.

An examination of Equation 3-13 indicates that the spiral transition curve is associated withfewer crashes and that this effect varies with radius. The AMF value is about 0.95 for curves witha radius of 500 ft. It increases to 0.98 for a radius of 3000 ft. The literature review did not identifyany research quantifying a similar relationship for spiral transitions on multilane highway curves.

Vertical Alignment

This subsection describes AMFs related to features of the highway’s vertical alignment. Atthis time, the only AMF addressed in this subsection is grade.

The relationship between grade and crash frequency was derived from the safety predictionmodels developed by Milton and Mannering (10) and by Harwood et al. (7). The Milton andMannering AMF is based on a mix of urban and rural multilane highways in Washington State. Thehighways were classified as principal arterials and had up to six lanes with ADTs of up to18,000 veh/d per lane. In contrast, the AMF from Harwood et al. (7) is based on rural two-lanehighways. They presented their AMF in tabular form. The two AMFs are compared in Figure 3-4.A best-fit trend line is shown for the tabulated data provided by Harwood et al. (7).

Figure 3-4. Grade AMF for Rural Highways.



AMFg ' (e b Pg & 1.0)Ps % 1.0 (3-14)

AMFlw, i ' e bi (Wl & 12) (3-15)

The Harwood AMF and the Milton and Mannering AMF can be described using Equation 3-14. The structure of this equation implies that the base condition for grade is 0 percent (i.e., flat).That is, flat highway segments have a grade AMF equal to 1.0. It should also be noted that the gradevariable is an absolute value implying that the AMF has the same value, regardless of whether thegrade is uphill or downhill.

where:AMFg = grade accident modification factor;

b = regression coefficient;Pg = percent grade (absolute value), %; andPs = proportion of crashes to which the AMF applies.

The values of variables b and Ps are provided in Table 3-6. For example, substitution of thevalues of 0.019 and 1.0 for b and Ps, respectively, results in the trend line shown in Figure 3-4 thatis attributed to Milton and Mannering (10).

Table 3-6. Coefficient Values for Grade on Rural Highways.Model Source Roadway Type Crash


Crash TypesSubset


bMilton &Mannering (10)

Urban & rural principalarterials

All All 1.0 0.019

Harwood et al. (7) Rural, 2-lane, undivided All All 1.0 0.016

The trend lines shown in Figure 3-4 indicate that the AMF for grade ranges from 1.0 for0 percent to 1.14 for 8 percent. Based on this analysis, the Harwood and the Milton and ManneringAMFs are reasoned to be applicable to two-lane and multilane highways, respectively.

Cross Section

Lane Width. This section describes the analysis of various lane width and shoulder widthAMFs derived from the literature. This analysis was broadened to include shoulder width becauseof its correlation with lane width. The findings from this analysis that relate to lane width arediscussed in this subsection. The findings for shoulder width are discussed in the next subsection.Most of the AMFs derived from the literature can be represented by the following functional form,where the base lane width is expressed as 12 ft:

where:AMFlw, i = lane width accident modification factor for roadway type i;

bi = regression coefficient for roadway type i; andWl = lane width, ft.



Some AMFs found in the literature were not directly adaptable to the generalized form ofEquation 3-15 (e.g., some specified discrete AMFs for specific lane widths). For these AMFs, log-linear regression was used with Equation 3-15 to quantify an equivalent value of bi. The variouscoefficients identified in the literature are identified in column 8 of Table 3-7, as are thecorresponding area type, road type, median type, and number of through lanes.

Table 3-7. Coefficient Analysis for Lane and Shoulder Width on Rural Highways.Design

ElementAreaType

RoadType

MedianType 1

Thru.Lanes

Model Source

CrashSeverity

SourceCoeff.bi 2, 3

Proportion4 BaseCoeff.bbPi Pb

Lane Rural Freeway Restrictive 4 Hadi et al. (2) Injury -0.3070 0.37 0.37 -0.3076 Hadi et al. (2) Injury -0.3390 0.49 0.37 -0.245

Highway Restrictive 4 Harwood et al. (11) All -0.029 0.36 0.36 -0.029Non-

Restrictive2 Harwood et al. (7) All -0.057 0.42 0.36 -0.049

Hadi et al. (2) Injury -0.0787 0.42 0.36 -0.067Vogt & Bared (3) Severe -0.1306 0.42 0.36 -0.111

4 Harwood et al. (11) All -0.043 0.37 0.36 -0.042Urban Street Non-

Restrictive2 Hadi et al. (2) Injury -0.0489 0.25 0.24 -0.0474 Hadi et al. (2) Injury -0.1037 0.18 0.24 -0.141

Shoulder Rural Freeway Restrictive 4 Hadi et al. (2) 5 Injury -0.0407 0.15 0.15 -0.041Freeway,Highway

Restrictive 4 Knuiman et al. (12) All -0.0352 0.16 0.16 -0.035Knuiman et al. (12) All -0.0460 0.16 0.16 -0.046

Highway Non-Restrictive

2 Harwood et al. (7) All -0.028 0.34 0.16 -0.013Vogt & Bared (3) Severe -0.0784 0.34 0.16 -0.036

Urban Freeway Restrictive 6 Hadi et al. (2) Injury -0.0594 0.14 0.16 -0.068Street Restrictive 4 Hadi et al. (2) Injury -0.0303 0.09 0.09 -0.030

Mix 4 Harwood (13) All -0.011 0.10 0.09 -0.010Non-Rest. 2 Hadi et al. (2) Injury -0.0489 0.17 0.09 -0.025

Notes:1 - Median type: non-restrictive - undivided, two-way left-turn lane, surfaced; restrictive - raised-curb, depressed.2 - Source coefficient: coefficient obtained directly from the literature for a specified combination of area type, road

type, median type, and through lanes.3 - Underlined coefficients represent a best-fit exponential curve to the reported AMFs that were tabulated for a range

of shoulder or lane widths by the researchers identified in the “Model Source” column.4 - Proportions are obtained from the crash database maintained by the State of Texas.5 - This coefficient applies to the inside shoulder; all other coefficients apply to the outside shoulder.

In a preliminary examination of the regression coefficients bi in Table 3-7, it was noted thatthey tended to vary among the various area and road types. In recognition of this wide range, it wasdecided that the most appropriate method of AMF development was to combine all of thecoefficients into one database and use linear regression to derive an equation for estimating bi as afunction of area type, road type, or both.




Pb

% 1.0 (3-16)

bb' ln (e bi & 1.0)Pb

Pi

% 1.0 (3-17)

As noted by Harwood et al. (7), lane width tends to influence specific types of crashes ontwo-lane, undivided highways. These “related” crashes include: single-vehicle run-off-road, samedirection sideswipe, and multiple vehicle opposite direction. It is likely that the multiple vehicleopposite direction crashes would not be influenced by lane width for depressed, or other types ofrestrictive, medians. Crashes related to shoulder width are most likely characterized as single-vehicle run-off-road crashes. More specifically, for outside shoulder width, the related crashes arelikely the single-vehicle run-off-road on right side. Similarly, for inside shoulder width, the relatedcrashes are likely single-vehicle run-off-road on left side. The proportion of these crash types Pi forthe corresponding design element, area type, road type, median type, and through lanes are listed incolumn 9 of Table 3-7. These proportions were obtained from the crash database maintained by theState of Texas, Department of Public Safety.

Based on the assumption that the proportion of crashes Pi can explain much of the variationin the coefficients bi due to median type and number of lanes, the following relationship was derivedto facilitate the estimation of an AMF for various combinations of area type and road type:




The values of Pi and Pb correspond to the crashes influenced by the AMF, and are both representedas a proportion of all crashes. The crash distribution used for Pi is that reflecting the crash historyof the roadway type corresponding to bi. The distribution used for Pb is that reflecting a specifiedbase combination of lanes and median type. For this analysis, a four-lane, depressed medianhighway was chosen to represent the base combination.

Equation 3-16 was combined with Equation 3-15 to obtain the following equation forestimating the “base coefficient” bb for a four-lane, depressed median highway with a specified areatype and road type:

The change in lane (or shoulder) width is specified to be 1.0 ft for all lane and median combinations.This equation was applied to both the lane width and shoulder width coefficients bi listed in Table 3-7 to estimate the base coefficient. Values of the base coefficient are listed in the last column ofTable 3-7. Theoretically, these coefficients have the effect of median type and number of lanesremoved and any systematic variability remaining can be explained by area type or road type.



bb ' &0.040 % 0.026 Is & 0.007 Ih,f (3-18)

AMFlw,b ' e &0.047 (Wl & 12) (3-19)

AMFlw, i ' (e &0.047 (Wl & 12)& 1.0)

Pi

0.36% 1.0 (3-20)

A regression analysis was undertaken to determine if area type or road type could explainany of the variability in the base coefficients. Weighted regression was used with the weight wj foreach variable equal to the reciprocal of the square of the corresponding base coefficient (i.e., wj =1/ bb, j

2). The following equation was developed as a result of this analysis:

where:bb = base coefficient for a four-lane, depressed median highway; Is = indicator variable for shoulder width (1 for shoulder width, 0 for lane width); and

Ih,f = indicator variable for road type (1 for highway or freeway, 0 for street).

The p-value for the Is coefficient is 0.029 and that for the Ih,f coefficient is 0.33. The weighted R2 is0.94. For rural highways, the value of bb that is applicable to lane width is computed fromEquation 3-18 as -0.047.

Based on the preceding analysis, the following equation represents the lane width AMF forthe base combination of lanes and median type (i.e., four-lane, depressed median highway). Thebase condition lane width for this AMF is 12 ft.


type (i.e., four-lane, depressed median highway).

Equation 3-19 can be combined with Equation 3-16 to obtain the lane width AMF for othercombinations of lanes and median type. The proportion of influential crashes for the basecombination Pb is 0.36. The resulting AMF is:

It can be tailored to a desired number of lanes and median type by using the variable Pi. Values forthis variable are listed in Table 3-8. The proportions in this table (and subsequent similar tables)were obtained from the crash database maintained by the State of Texas, Department of PublicSafety.

Table 3-8. Crash Distribution for Rural Highway Lane Width AMF.Median Type Crash Type Subset Through Lanes Subset Proportion

Depressed Single-vehicle run-off-road, same direction sideswipe

4 0.366 0.35

Undivided, TWLTL, or flush paved

Single-vehicle run-off-road, same direction sideswipe,

multiple vehicle opposite direction

2 0.42

4 0.37



0.6

0.8

1.0

1.2

1.4

1.6

9 9.5 10 10.5 11 11.5 12

Lane Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

2-Lane Highway (Vogt & Bared [3])

2-Lane Highway (Hadi et al. [2])

2-Lane Highway (Harwood et al. [7])

2-Lane Highway (derived)

0.95

1.00

1.05

1.10

1.15

1.20

1.25

0 500 1000 1500 2000 2500 3000

Average Daily Traffic Volume, veh/d

Acc

iden

t Mod

ifica

tion

Fact

or

9-ft or less

10-ft lanes

11-ft lanes

12-ft or more

0.6

0.8

1.0

1.2

1.4

1.6

9 9.5 10 10.5 11 11.5 12

Lane Width, ftA

ccid

ent M

odifi

catio

n Fa

ctor

Multilane HighwayHarwood et al. (11)

Multilane Highway (derived)

The AMFs obtained from Equation 3-20 are illustrated in Figure 3-5. They are labeled“derived” and have a bold line weight. They are compared to the AMFs developed by otherresearchers. The trend is one of increasing AMF value with a reduction in lane width. For a givenlane width, the derived AMF for two-lane highways is larger than that for multilane highways. Thereis general agreement between the derived AMFs and those reported in the literature. Significantdifferences between AMFs are likely a reflection of bias (due to colinearity) in the original models.


Figure 3-5. Lane Width AMF for Rural Highways.

An expert panel convened by Harwood et al. (7) rationalized that lane width would not haveas significant an effect on crash frequency at low volume as at higher volume. The general trendbetween lane width AMF and ADT suggested by this panel is shown in Figure 3-6. It has beenmodified to converge to the AMF obtained from Equation 3-20 for ADTs of 2000 veh/d or more.

Figure 3-6. Lane Width AMF for Low Volume Rural Highways.



AMFosw,b ' e &0.021 (Ws & 8) (3-21)

AMFosw, i ' ( e &0.021 (Ws & 8)& 1.0)

Pi

0.16% 1.0 (3-22)

Outside Shoulder Width. The following equation represents the shoulder width AMF forthe base combination of lanes and median type (i.e., four-lane, depressed median highway). It wasderived in a similar manner as the lane width AMF. The base condition shoulder width is 8 ft.

where:AMFosw, b = outside shoulder width accident modification factor for the base combination of lanes

and median type (i.e., four-lane, depressed median highway); andWs = outside shoulder width, ft.

Equation 3-21 can be combined with Equation 3-16 to obtain the outside shoulder widthAMF for other combinations of lanes and median type. The proportion of influential crashes for thebase combination Pb is 0.16. The resulting AMF is:


Table 3-9. Crash Distribution for Rural Highway Outside Shoulder Width AMF.Median

TypeCrash Type Subset Through

LanesSubset

ProportionDepressed Single-vehicle run-off-road, right side 4 0.16

6 0.15Undivided, TWLTL,

or flush pavedSingle-vehicle run-off-road, either side 2 0.34

4 0.27

The AMFs obtained from Equation 3-22 are illustrated in Figure 3-7. They are labeled“derived” and have a bold line weight. They are compared to the AMFs developed by otherresearchers. The trend is one of increasing AMF value with a reduction in shoulder width. For agiven shoulder width, the AMF for two-lane highways is larger than that for multilane highways.There is general agreement between the derived AMFs and those reported in the literature.Significant differences between AMFs are likely a reflection of bias (due to colinearity) in theoriginal models.

A shoulder width AMF was derived from the model developed by Wang et al. (4). However,it was very sensitive to shoulder width. In fact, it has a value of 2.1 when the shoulder width is0.0 ft, which is much higher than the values obtained from other AMFs. An examination of the dataevaluated by Wang et al. indicated that only 4 percent of the segments had shoulder widths less than4 ft, yet these same segments account for 20 percent of the crashes. Hence, it is likely that there areunspecified factors that underlie this over-representation of crashes when categorized by shoulderwidth. For these reasons, the AMF derived from the Wang model was not considered further.



0.8

1.0

1.2

1.4

1.6

1.8

0 2 4 6 8 10


Acc

iden

t Mod

ifica

tion

Fact

or 2-Lane Highway (Vogt & Bared [3])

2-Lane Highway (Harwood et al. [7])

2-Lane Highway (derived)

0.8

1.0

1.2

1.4

1.6

1.8

0 2 4 6 8 10


Acc

iden

t Mod

ifica

tion

Fact

or

Multilane Highway (Knuiman et al. [12])


0.95

1.05

1.15

1.25

1.35

1.45

0 500 1000 1500 2000 2500 3000

Average Daily Traffic Volume, veh/d

Acc

iden

t Mod

ifica

tion

Fact

or No shoulders

2-ft shoulders

4-ft shoulders

6-ft shoulders

8-ft or more


Figure 3-7. Outside Shoulder Width AMF for Rural Highways.

An expert panel convened by Harwood et al. (7) used engineering judgment to limit the AMFthey developed based on roadway volume. They rationalized that for very low traffic volumes,shoulder width would not have as significant an effect on crash frequency as at higher volumes. Therelationship between shoulder width AMF and ADT suggested by this panel is based on a baseshoulder width of 6 ft. It was converted to a base shoulder width of 8 ft for this document and isshown in Figure 3-8. This figure would be used instead of Equation 3-22 for ADTs of 2000 veh/dor less.

Figure 3-8. Outside Shoulder Width AMF for Low Volume Rural Highways.



AMFisw, i ' ( e &0.021 (Wis & 4)& 1.0)

Pi

0.16% 1.0 (3-23)

Inside Shoulder Width. A review of the literature did not reveal any AMFs or safetyprediction models that address the inside shoulder width of a rural highway. A model based on ruralfreeways was developed by Hadi et al. (2). It included a variable for inside shoulder width.However, when the regression coefficient associated with this variable was compared withcoefficients for outside shoulder width (see Table 3-7), no significant difference was found betweencoefficients. Hence, Equation 3-21 is rationalized to be equally applicable to inside shoulder width,after adjustment for a base width of 4 ft. Equation 3-21 was combined with Equation 3-16 to obtainthe following inside shoulder width AMF:

where:AMFisw = inside shoulder width accident modification factor; and

Wis = inside shoulder width, ft.

The proportion of influential crashes for the base combination Pb is 0.16. Equation 3-23 can betailored to the desired number of lanes and median type by using the variable Pi. The value of thisvariable is selected from Table 3-10.

Table 3-10. Crash Distribution for Rural Highway Inside Shoulder Width AMF.Facility Type Median


LanesSubset

ProportionRural

highwayDepressed Single-vehicle run-off-road, left side 4 0.16

6 0.15

The AMF obtained from Equation 3-23 is illustrated in Figure 3-9. It is labeled “derived”and has a bold line weight. It is compared to the AMFs developed by Hadi et al. (2). The trend isone of increasing AMF value with a reduction in shoulder width. There is general agreementbetween the derived AMF and that derived from the Hadi model.

Median Width. AMFs for median width were developed from safety prediction modelsdeveloped by Hadi et al. (2) and Wang et al. (4), and from data reported by Knuiman et al. (12). TheHadi and Wang AMFs are based on models developed for rural divided highways. Knuiman et al.examined crash data for a mix of rural freeways, urban freeways, and major highways. The crashrate adjustment factors (analogous to AMFs) they computed are shown in Figure 3-10, as are the“best-fit” trend lines. It should be noted that none of the researchers examined the relationshipbetween median type (i.e., surfaced, depressed) and crash frequency.

Equation 3-24 was developed to represent the AMFs derived from the literature. The basecondition for this AMF is a median width of 76 ft for depressed medians and 16 ft for surfacedmedians (i.e., TWLTL or flush paved). The coefficients used in this model are listed in columns 4through 6 of Table 3-11.



0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 100

Median Width, ft

Rel

ativ

e Ef

fect

on

Inju

ry C

rash

es

Illinois Data

Utah Data

AMFmw 'b0 (e b1 W

b2m & 1.0) % 1.0

b0 (e b1 Wb2

mb & 1.0) % 1.0(3-24)

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10

Inside Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Rural Freeway (Hadi et al. [2])


Figure 3-9. Inside Shoulder Width AMF for Rural Highways.

Figure 3-10. Relationship between Median Width and Severe Crash Frequency.

where:AMFmw = median width accident modification factor;

Wmb = base median width (16 ft for surfaced median; 76 ft for depressed median), ft; andWm = median width, ft.



0.6

0.8

1.0

1.2

1.4

1.6

5 10 15 20 25 30

Median Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Illinois, 4-Lane (Knuiman et al.[12])

4-Lane (Wang et al.[4])

Utah, 4-Lane (Knuiman et al. [12])

4-Lane (Hadi et al. [2])

Derived

Table 3-11. Coefficient Values for Median Width on Rural Highways.Model Source Roadway Type Crash


Coeff.b0 b1 b2 Wm< 40ft Wm> 40ft

Hadi et al. (2) Rural, 4-lane, highway All 1.0 -0.0458 0.5 -0.046 -0.046Knuiman et al.(12)

Urban & rural, 4-lane, highway (Utah) Severe 0.488 -0.00111 2.0 -0.153 -0.055Urban & rural, 4-lane, highway (Illinois) Severe 0.483 -0.00020 2.0 -0.042 -0.111

Wang et al. (4) Rural, 4-lane, highway All 1.0 -0.003 1.0 -0.029 -0.046Weighted Average: -0.038 -0.052

Figure 3-11 illustrates the AMFs listed in Table 3-11. They have a base condition medianwidth of 16 ft. Similar trends are obtained for a base width of 76 ft. The AMFs are in generalagreement. The AMF from Knuiman et al. using Utah data is less in agreement and indicates agreater sensitivity to median width for widths of 40 ft or less.

Figure 3-11. Median Width AMF for Rural Highways.

The derived AMF relationship is shown in Figure 3-11. It is based on Equation 3-24 withb0 = 1.0, b2 = 0.5, and the weighted average of the equivalent b1 coefficients listed in columns 7 and8 of Table 3-11 (where the weight w for each coefficient is equal to its reciprocal squared [i.e., w =1/b2]). The equivalent b1 coefficient for each model source was derived from a regression analysisusing Equation 3-24 with b0 = 1.0 and b2 = 0.5 for median widths ranging from 10 to 40 ft. Theanalysis was repeated for median widths ranging from 40 to 80 ft. The AMFs obtained fromEquation 3-24 (using the base coefficients) served as the dependent variable.

Shoulder Rumble Strips. Griffith (14) investigated the correlation between the presenceof continuous rolled-in rumble strips and crash frequency on rural freeways in Illinois. The focusof his investigation was on single-vehicle run-off-road crashes. The reported AMFs are shown in



AMFsrs ' (0.93 & 1.0) Pi % 1.0 (3-25)

column 5 of Table 3-12. It is rationalized that these factors are also applicable to rural highways.The standard deviation for the AMF value of 0.93 in Table 3-12 indicates the AMF is notsignificantly different from 1.0. However, the AMF value is only slightly larger than that used forfreeways in Chapter 2 (and which is more confidently known) and is reasoned to be a conservativeestimate of the relationship between rumble strips and severe crashes on rural highways.

Table 3-12. AMFs for Shoulder Rumble Strips on Rural Highways.Data

SourceState Crash Severity Crash Type Subset Base AMF (frs) Standard

DeviationGriffith (14) Illinois All Single-vehicle run-off-road 0.79 0.10

Injury Single-vehicle run-off-road 0.93 0.15

The shoulder rumble strip AMF can be computed using Equation 3-25. It is based on theoverall base AMF for severe crashes in Table 3-12. For Texas applications, it requires theappropriate crash distribution proportion for the roadway type of interest. These proportions arelisted in Table 3-13.

where:AMFsrs = shoulder rumble strip accident modification factor; and

Pi = proportion of influential crashes that occur on roadway type i (from Table 3-13).

Table 3-13. Crash Distribution for Rural Highway Shoulder Rumble Strip AMF.Median


LanesSubset

ProportionDepressed Single-vehicle run-off-road, either side 4 0.32


or flush pavedSingle-vehicle run-off-road, right side 2 0.17

4 0.13

Centerline Rumble Strip. Persaud et al. (15) investigated the effect of continuous centerlinerumble strips on crash frequency for rural two-lane highways in seven states. The reported crashreduction factors were converted to AMFs for this chapter; these values are shown in column 4 ofTable 3-14. It is rationalized that these factors are also applicable to multilane, undivided highways.

Table 3-14. AMFs for Centerline Rumble Strip on Rural Two-Lane Highways.Data Source Crash Severity Crash Type Subset Base AMF Standard

DeviationPersaud (15) Injury All 0.86 0.07

All All 0.88 0.06



AMFcrs ' 0.86 (3-26)

AMFT ' 1.0 & 0.7 PD PLT/D (3-27)

PD '0.0047 Dd % 0.0024 D 2

d

1.199 % 0.0047 Dd % 0.0024 D 2d

(3-28)

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15 20

Driveway Density, driveways/mi

Acc

iden

t Mod

ifica

tion

Fact

or

Rural, 2-Lane (based on Harwood et al.[7])

Given the preference for AMFs based on severe crash data, the two-lane highway centerlinerumble strip AMF is:

where:AMFcrs = centerline rumble strip accident modification factor.

TWLTL Median Type. Harwood et al. (7) developed an AMF to capture the effect ofdriveway activity on crash frequency, as it relates to the addition of a TWLTL to an undivided two-lane highway. This AMF is shown as Equation 3-27.

with,

where:AMFT = TWLTL accident modification factor;

PD = driveway-related crashes as a proportion of total crashes; andPLT/D = left-turn accidents susceptible to correction by a TWLTL as a proportion of driveway-

related crashes (estimated as 0.50).

Equation 3-28 represents the ratio of driveway-related crash rate to total crash rate.

The AMF for adding a TWLTL to a rural highway is shown in Figure 3-12. The trend lineattributed to Harwood et al. (7) is based on Equations 3-27 and 3-28. It indicates that the TWLTLis more effective at reducing crashes as driveway density increases.

Figure 3-12. TWLTL Median Type AMF for Rural Highways.



Superelevation. Harwood et al. (7) developed an AMF to describe the relationship betweensuperelevation rate and crash frequency. Their analysis indicated that crash frequency was higheron highways that were deficient in the amount of superelevation provided. Superelevation deficiencywas computed as the difference between the superelevation provided on the curve and that specifiedin the AASHTO document A Policy on Geometric Design of Highways and Streets (16) (GreenBook). Crash frequency was found to be higher with increasing superelevation deficiency.

Harwood et al. (7) convened an expert panel to review the relationship betweensuperelevation deficiency and crash frequency. They determined that curves with a superelevationdeficiency of 1.0 percent or less would not likely experience an increase in crashes, as suggested bythe crash data analysis. The AMF values for superelevation deficiency that are recommended by theexpert panel are listed in Table 3-15. If the existing (or proposed) superelevation rate equals orexceeds that recommended in the AASHTO Green Book, then the AMF is 1.0.

Table 3-15. AMFs for Superelevation on Rural Highways.Superelevation Deficiency, 1 %

0.0 or less 1.0 2.0 3.0 4.0 5.0AMFe: 1.00 1.00 1.06 1.09 1.12 1.15

Note:1 - Superelevation deficiency = AASHTO Policy superelevation rate ! existing (or proposed) superelevation rate.

Passing Lanes. Harwood et al. (7) developed an AMF to describe the relationship betweenpassing lane presence and crash frequency. Their analysis indicated that crash frequency was loweron two-lane highways to which a passing lane was added. They focused their evaluation on two typesof passing lanes: (1) conventional passing lane or climbing lane added in one direction of a two-lanehighway and (2) short four-lane section specifically built to provide passing opportunities in bothdirections. The climbing lane or passing lane is assumed to satisfy warrants for such lanes and hasa length that is sufficient to provide safe and efficient passing opportunities. Guidelines describingjustification criteria and length considerations for climbing lanes and passing lanes are provided inthe Green Book (16).

The AMFs for passing lanes AMFpass are listed in Table 3-16. They are not applicable tothree- or four-lane cross sections having a length that extends beyond that needed to provide safe andefficient passing operation.

Table 3-16. AMFs for Passing Lanes on Rural Two-Lane Highways.Climbing Lane or Passing Lane Type 1

One Direction (three-lane cross section) Two Directions (four-lane cross section)AMFpass: 0.75 0.65

Note:1 - Only applicable to highway segments where the passing lane is warranted and has a length that is sufficient to

provide safe and efficient passing opportunities (no more and no less).



AMFhc ' (e b (Whc& 30)& 1.0) Ps % 1.0 (3-29)

Roadside Design

This section describes AMFs related to the roadside design of a rural highway segment.Topics specifically addressed are listed in Table 3-17. Many roadside design components orelements that are not listed in this table (e.g., ditch shape) are also likely to have some correlationwith severe crash frequency on the highway segment. However, a review of the literature did notreveal that their effect has been quantified by previous research. The list of available AMFs forhighway roadside design is likely to increase as new research in this area is undertaken.

Table 3-17. AMFs Related to Roadside Design of Rural Highways.Section Accident Modification Factor

Cross section Horizontal clearance Side slope Utility pole densityBridge width

Appurtenances see text


Cross Section

Horizontal Clearance. The relationship between horizontal clearance distance and single-vehicle run-off-road crashes was evaluated by Miaou (18). He developed a safety prediction modelfor rural highways that included this distance as a variable. The AMF derived from this model isdescribed in Equation 3-29. The base condition for this AMF is a horizontal clearance of 30 ft.

where:AMFhc = horizontal clearance accident modification factor; and

Whc = horizontal clearance (average for length of segment), ft.

The value of variable b is provided in Table 3-18. The subset proportions appropriate forTexas rural highway applications are provided in Table 3-19. For four-lane divided highways,Equation 3-29 yields an AMF that ranges from 1.05 at 10 ft clearance to 0.95 at 60 ft clearance.



AMFss ' (e b (1/Ss & 1/4)& 1.0) Ps % 1.0 (3-30)

Table 3-18. Coefficient Values for Horizontal Clearance on Rural Highways.ModelSource

Roadway Type CrashSeverity

Subset of Influenced Crash Types

SubsetProportion, Ps

Coefficient b

Miaou (18) Rural, 2-lane, undivided All Single-vehicle run-off-road unreported -0.0137

Table 3-19. Crash Distribution for Rural Highway Horizontal Clearance Width AMF.Median


LanesSubset

ProportionDepressed Single-vehicle run-off-road, right side 4 0.16


or flush pavedSingle-vehicle run-off-road, either side 2 0.34

4 0.27

Side Slope. The relationship between side slope and crash frequency was evaluated byMiaou (18). He developed a safety prediction model for rural highways that included side slope asa variable. The AMF derived from this model is described in Equation 3-30. The base conditionfor this AMF is a side slope of 1V:4H (i.e., Ss = 4.0).

where:AMFss = side slope accident modification factor; and

Ss = horizontal run for a 1 ft change in elevation (average for length of segment), ft.

The value of variable b is provided in Table 3-20. The subset proportions appropriate forTexas rural highway applications are provided in Table 3-19. For four-lane divided highways,Equation 3-30 yields an AMF that ranges from 1.00 at 1V:4H to 1.01 at 1V:3H.

Table 3-20. Coefficient Values for Side Slope on Rural Highways.ModelSource




Coefficient b

Miaou (18) Rural, 2-lane, undivided All Single-vehicle run-off-road unreported 0.692

Utility Pole Density. The relationship between utility pole density and crash frequency wasevaluated by Zegeer and Parker (19). They developed a safety prediction model for rural and urbanroads in four states. The model included average pole offset, traffic volume, and pole density asindependent variables. The AMF derived from this model is described in Equation 3-31. Detailsof the model are described in Table 3-21. The base condition is 25 poles/mi and a pole offset of30 ft.



AMFpd ' (fp & 1.0) Ps % 1.0 (3-31)

fp '(0.0000984 ADT % 0.0354 Dp ) W &0.6

o & 0.040.0000128 ADT % 0.075

(3-32)

with,



Table 3-21. Coefficient Values for Utility Pole Density on Rural Highways.Model Source Roadway Type Crash

SeveritySubset of



The subset proportions appropriate for Texas rural highway applications are provided inTable 3-22. Equation 3-31 yields an AMF that ranges from 1.08 at a pole density of 50 poles/mi andoffset of 10 ft to 0.99 at a pole density of 10 poles/mi and offset of 30 ft. The AMF is more sensitiveto pole offset than it is to density or average daily traffic volume.

Table 3-22. Crash Distribution for Rural Highway Utility Pole Density AMF.Median


LanesSubset

ProportionDepressed Single-vehicle collision with pole 4 0.054


or flush pavedSingle-vehicle collision with pole 2 0.038

4 0.048

Bridge Width. Turner (20) evaluated the relationship between bridge width and bridge crashrate for rural two-lane highways in Texas. “Relative bridge width” was defined as the differencebetween the bridge width and the approach traveled-way width. Bridge width was measuredbetween the face of the bridge rails. Traveled-way width is the pavement width available for vehiclemovement, exclusive of paved shoulders and auxiliary lanes. Approach traveled-way width is thetraveled-way width of the normal highway cross section, prior to any change in cross sectionassociated with the bridge approach.

The relationship between relative bridge width and crash rate, as reported by Turner (20), isshown in Figure 3-13 using circular data points. Crash rate is defined as bridge-related crashes per



AMFbw ' (e b Ibr (Wb & 12)& 1.0) Ps % 1.0 (3-33)

y = 0.4667e-0.1346x

R2 = 0.9931

0.00

0.20

0.40

0.60

0.80

1.00

1.20

-6 -4 -2 0 2 4 6 8 10 12 14

Relative Bridge Width, ft

Brid

ge C

rash

es/M

V

million vehicles (mv). A best-fit trend line and corresponding equation are also shown. The AMFderived from this model is described in Equation 3-33. The base condition is a relative bridge widthof 12 ft, which is consistent with an 8 ft outside shoulder, a 4 ft inside shoulder, and no reductionin traveled-way width across the bridge.

where:AMFbw = bridge width accident modification factor;

Ibr = presence of bridges (1 if one or more bridges present, 0 if not); andWb = relative bridge width (= bridge width !approach traveled-way width), ft.

Figure 3-13. Correlation between Relative Bridge Width and Bridge Crash Rate.

The value of variable b is provided in Table 3-23. The subset proportions appropriate fortwo-lane highway applications are provided in Table 3-24.

Table 3-23. Coefficient Values for Bridge Width on Rural Highways.ModelSource




Coef-ficient b

Turner (20) Rural, 2-lane, undivided All Single-vehicle collision with bridge unreported -0.135

Table 3-24. Crash Distribution for Rural Highway Bridge Width AMF.Median


LanesSubset

ProportionUndivided, TWLTL,

or flush pavedSingle-vehicle collision with bridge 2 0.017

4 0.011



Appurtenances

As discussed previously, AMFs for roadside safety appurtenances are not described in thischapter. The safety literature related to roadside appurtenances has focused on the informationneeded to evaluate the cost-effectiveness of installing individual appurtenances at specific locations.Most of the research conducted in this area has been incorporated into a complex and comprehensiveprocedure for evaluating appurtenances on a case-by-case basis. This procedure is outlined in areport by Mak and Sicking (21) and automated in the Roadside Safety Analysis Program (RSAP)(22).

RSAP can be used to evaluate alternative roadside safety appurtenances on individual roadsegments. The program accepts as input information about the road segment geometry and trafficcharacteristics. It also allows the analyst to describe the roadside cross section, location of fixedobjects, and safety appurtenance design. Table 3-25 summarizes the various RSAP inputs. Theoutput from RSAP includes an estimate of annual crash frequency as well as the road-user costsassociated with these crashes. The crash reduction potential realized by adding a roadside safetyappurtenance (or changing the roadside cross section) can be estimated by specifying the changedcondition as an “alternative.”





-- Traffic volume (ADT) Truck percentageTraffic growth factor

Geometricdesign



Roadsidedesign






AMFdd '0.20 % [0.05 & 0.005 ln(ADT)] Dd 0.622

0.20 % [0.05 & 0.005 ln(ADT)] Dbase 0.622 (3-34)

AMFdd ' (e b (Dd & Dbase )& 1.0) Ps % 1.0 (3-35)

Access Control

This section is devoted to AMFs related to the access control elements of a rural highway.A review of the literature indicates that median type and driveway density have an influence on crashfrequency. The correlation between median type and crashes is addressed previously in the sectiontitled TWLTL Median Type. This section on access control describes the correlation betweendriveway density and crash frequency.

Four accident modification factors for driveway density were identified during the literaturereview. The first is offered by Harwood et al. (7). It was developed for rural two-lane highways andis based on an analysis by Hauer (23) of crash rates published by others. The equation described byHarwood et al. (7) is listed herein as Equation 3-34. The constant “0.622” was added to reflect thefact that the original form of the model used a driveway density variable that was based on units of“driveways/km.”

where:AMFdd = driveway density accident modification factor; and

Dbase = base driveway density, driveways/mi.

The remaining three AMFs for driveway density were derived from safety prediction modelsdeveloped by Vogt and Bared (3), Harwood et al. (7), and Wang et al. (4). The models by Vogt andBared and by Harwood et al. are based on two-lane, undivided highway segments. The model byWang et al. is based on four-lane, divided highways. The generalized AMF is shown below. Valuesof the variables b and Ps are provided in Table 3-26.

Table 3-26. Coefficient Values for Driveway Density for Rural Highways.Model Source Roadway Type Crash


Crash TypesSubset


bVogt & Bared (3) Rural, 2-lane, undivided Severe All 1.0 0.0062Harwood et al. (7) Rural, 2-lane, undivided All All 1.0 0.0084

Weighted Average: 0.0070Wang et al. (4) Rural, 4-lane, divided All All 1.0 0.034

All four AMFs are compared in Figure 3-14 for a base driveway density offive driveways/mi. The trends in the data indicate that the relationship between driveway density



AMFdd ' e 0.007 (Dd & 5) (3-36)

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10 12 14 16


Acc

iden

t Mod

ifica

tion

Fact

or

2-Lane, Undivided (Equation 3-34) 500 veh/d 5000 veh/d

2-Lane, Undivided(Vogt & Bared [3])

4-Lane, Divided (Wang et al. [4])

Derived

2-Lane, Undivided(Table 3-26, Harwood et al. [7])

and crashes varies widely. This variation is likely due to the fact that driveway activity level (i.e.,driveway traffic demand) is not used in the models. Equation 3-34 exhibits an illogical trend suchthat, for a given driveway density, the AMF value decreases with increasing daily traffic demand.Logically, the driveway volume should increase with increasing daily traffic demand, which shouldincrease the risk of a collision.

Figure 3-14. Driveway Density AMF for Rural Highways.

The two, two-lane highway AMFs in Table 3-26, show less sensitivity to driveway densitythan the four-lane highway AMF attributed to Wang et al. It is possible that crash frequency on four-lane highways is more sensitive to driveway density. However, it is also possible that the data fromwhich these AMFs were derived inadvertently introduced some bias due to unspecified variables thatare correlated with driveway density.

A weighted average of the coefficients for the two AMFs based on two-lane, undividedhighways yields a value of 0.007. The weight w used for this average equals the reciprocal of thecoefficient squared (i.e., w = 1/b2). It is unclear whether the correlation between driveway densityand AMF value varies with highway cross section. Based on this analysis, the best-fit AMF fordriveway density on rural two-lane highways is:

At this time, it rationalized that this AMF represents the best estimate of the relationship betweendriveway density and crash frequency for multilane rural highways.



AMFsl ' e b (V & 55) (3-37)


This section describes AMFs related to features of the highway that are not categorized asrelated to geometric design or roadside design. At this time, the only AMF addressed in this sectionis speed limit.

Two safety prediction models developed for rural highways were found to have a variablefor speed limit. One of these models was developed by Hadi et al. (2). Another was that developedby Milton and Mannering (10). A generalized AMF form is shown in Equation 3-37 for a base speedlimit of 55 mph. It can be used to represent the AMF obtained from both of the two predictionmodels by proper substitution of the coefficient b from Table 3-27.

where:AMFsl = speed limit accident modification factor; and

V = speed limit, mph.

The two AMFs are compared in Figure 3-15. The two coefficients for all model sources areso similar that they plot as one trend line. The trends in the figure indicate that higher speed limitsare associated with fewer severe crashes. Although not shown in the figure, similar trends have beenfound in safety prediction models developed for urban streets. It is likely that an increase in speedlimit does not make the highway safer; rather, it probably indicates that highways with a higher speedlimit tend to have a more generous design.

Table 3-27. Coefficient Values for Speed Limit for Rural Highways.Model Source Roadway Type Crash


Crash TypesCoefficient b

Hadi et al. (2) Rural, 2-lane, highway Injury All -0.0108Milton & Mannering (10) Urban & rural, principal arterials All All -0.0111 1

-0.0103 Weighted Average: -0.011

Note:1 - Separate safety prediction models were developed for data from principal arterials in the eastern and western half

of Washington State.

The derived AMF relationship is shown in Figure 3-15. It uses the weighted average of theb coefficients listed in Table 3-27 (where the weight w for each coefficient is equal to its reciprocalsquared [i.e., w = 1/b2]). There is insufficient data to determine if this coefficient varies by number-of-lanes or median type. Hence, the derived AMF is offered as approximate for all lanes and mediantypes until new information becomes available.



0.4

0.6

0.8

1.0

1.2

1.4

40 45 50 55 60 65 70

Speed Limit, mph

Acc

iden

t Mod

ifica

tion

Fact

or


Rural, 2-Lane Highways(Hadi et al. [2])

Undivided & Divided Highways (derived)

Figure 3-15. Speed Limit AMF for Rural Highways.

REFERENCES


2. Hadi, M.A., J. Aruldhas, L-F. Chow, and J.A. Wattleworth. “Estimating Safety Effects of Cross-Section Design for Various Highway Types Using Negative Binomial Regression.”Transportation Research Record 1500. Transportation Research Board, Washington, D.C.,1995, pp. 169-177.

3. Vogt, A., and J. Bared. Accident Models for Two-Lane Rural Roads: Segments andIntersections. Report No. FHWA-RD-98-133. Federal Highway Administration, Washington,D.C., October 1998.

4. Wang, J., W.E. Hughes, and R. Stewart. Safety Effects of Cross-section Design for Rural, Four-Lane, Non-Freeway Highways. Report No. FHWA-RD-98-071. Federal HighwayAdministration, Washington, D.C., May 1998.

5. Zegeer, C., H. Huang, J. Stewart, R. Pfefer, and J. Wang. “Effects of a Tow-Away ReportingThreshold on Crash Analysis Results.” Transportation Research Record 1635. TransportationResearch Board, Washington, D.C., 1998, pp. 49-57.

6. Zegeer, C.V., R. Stewart, D. Reinfurt, F.M. Council, T. Neuman, E. Hamilton, T. Miller, and W.Hunter. Cost-Effective Geometric Improvements for Safety Upgrading of Horizontal Curves.Report No. FHWA-RD-90-021. Federal Highway Administration, Washington, D.C., 1990.




8. Raff, M. “Interstate Highway-Accident Study.” Highway Research Board Bulletin 74. HighwayResearch Board, Washington, D.C., 1953.

9. Bonneson, J.A. “Working Paper 7 - Side Friction Demand: A Balance Between Speed andComfort.” Quarterly Progress Report, NCHRP Project 15-16, Superelevation DistributionMethods and Transition Designs. Texas Transportation Institute, College Station, Texas, June1988.

10. Milton, J., and F. Mannering. The Relationship between Highway Geometrics, Traffic RelatedElements, and Motor Vehicle Accidents. Report No. WA-RD 403.1. Washington StateTransportation Center, University of Washington, Seattle, Washington, March 1996.

11. Harwood, D.W., E.R. Kohlman Rabbani, K.R. Richard, H.W. McGee, and G.L. Gittings.NCHRP Report 486: Systemwide Impact of Safety and Traffic Operations Design Decisions for3R Projects. Transportation Research Board, Washington, D.C., 2003.

12. Knuiman, M.W., F.M. Council, and D.W. Reinfurt. “Association of Median Width andHighway Accident Rates.” Transportation Research Record 1401. Transportation ResearchBoard, Washington, D.C., 1993, pp. 70-82.

13. Harwood, D.W. NCHRP Report 282: Multilane Design Alternatives for Improving SuburbanHighways. Transportation Research Board, Washington, D.C., 1986.

14. Griffith, M.S. “Safety Evaluation of Rolled-In Continuous Shoulder Rumble Strips Installed onFreeways.” Transportation Research Record 1665. Transportation Research Board, Washington,D.C., 1999, pp. 28-34.

15. Persaud, B.N., R.A. Retting, and C.A. Lyon. “Crash Reduction Following Installation ofCenterline Rumble Strips on Rural Two-Lane Roads.” Accident Analysis and Prevention.Vol. 36, 2004, pp. 1073-1079.

16. A Policy on Geometric Design of Highways and Streets. American Association of StateHighway and Transportation Officials, Washington, D.C., 2004.


18. Miaou, S.P. Measuring the Goodness-of-Fit of Accident Prediction Models. Report No. FHWA-RD-96-040. Federal Highway Administration, Washington, D.C., 1996.




20. Turner, D.S. “Prediction of Bridge Accident Rates.” Journal of Transportation Engineering.Vol. 110, No. 1. American Society of Civil Engineers, Washington, D.C., January 1984, pp. 45-54.



23. Hauer, E. “Access and Safety.” Unpublished web document. Available athttp://roadsafetyresearch.com. April 2001.

Chapter 4 Urban Streets


Chapter 4Urban Streets

Page


SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4Harwood Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5Hadi Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7Hauer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8Bonneson and McCoy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10Comparison of Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14

Horizontal Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16

Lane Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17Median Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19TWLTL Median Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20Curb Parking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23Uncurbed Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25

Roadside Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27Appurtenances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29

Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Truck Presence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31Speed Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33



INTRODUCTION

The urban street is intended to provide both mobility to through travelers and access toadjacent properties. It is also intended to serve motorists, transit riders, pedestrians, and bicyclistswithin the right-of-way. As consequence of this mixture of function and travel mode, the urbanstreet has a complex design that is challenged to serve all modes in an equally safe and efficientmanner. The high cost of right-of-way presents additional challenges to the development of a designthat is not only safe and efficient but also cost-effective.

The development of a safe, efficient, and economical urban street design typically reflectsthe consideration of a wide variety of design alternatives. A variety of techniques exist forestimating the operational benefits of alternatives; many are automated through software tools.Techniques for estimating construction and right-of-way costs are also available to the designer.Unfortunately, techniques for estimating the safety benefits of alternative designs are not as readilyavailable. This chapter summarizes information in the literature that can be used to estimate the crashfrequency associated with various urban street design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various urban street design components and safety. Thisinformation is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in Chapter 4 of the RoadwaySafety Design Workbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical urban street segment. They include variables for traffic volume and segmentlength. They also include variables for other factors considered to be correlated with crash frequency(e.g., median type, land use, etc.). One or more AMFs can be multiplied by the expected crashfrequency obtained from the prediction model to produce an estimate of the expected crash frequencyfor a specific street segment.

Scope

This chapter addresses the safety of urban street segments. It does not address the safety ofintersections on these streets. For this reason, the crashes addressed herein are referred to as “mid-block” crashes. Crashes that occur at, or are related to, urban intersections are the subject ofChapter 7.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a widevariation in reporting threshold among cities and states. This variation complicates the extrapolationof crash trends found in one location to another location. Moreover, it can confound thedevelopment of safety prediction models using data from multiple agencies. Reporting threshold



is strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given street will be lowif it is located in an area with a high reporting threshold. In contrast, this same street will have a highcrash frequency if it is located in an area with a low reporting threshold. This problem is minimizedwhen crash data analyses, comparisons, and models are based on severe crash data.

The relationships described in this chapter address the occurrence of vehicle-related crasheson urban streets. They assume that the distribution of pedestrian and bicycle crashes remainsunchanged, regardless of a change in street design or traffic volume. Relationships that specificallyfocus on vehicle-pedestrian and vehicle-bicycle crashes on streets are not addressed.

Overview

This chapter documents a review of the literature related to urban street safety. The focusis on quantitative information that relates severe crash frequency to various geometric designcomponents of the urban street. The review is not intended to be comprehensive in the context ofreferencing all works that discuss urban street safety. Rather, the information presented herein isjudged to be the most current information that is relevant to urban street design in Texas. It is alsojudged to be the most reliable based on a review of the statistical analysis techniques used and theexplanation of trends.


This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various urban street design components and severe crashfrequency. As noted previously, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 4 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels reported in the literature are described. In the second part, accident modification factors aredescribed. Within this part, the various factors examined are organized into the following categories:roadway geometric design, roadside design, and access control.


Described in this part of the chapter are several models that were developed to estimate theexpected frequency of crashes on urban street segments. The first three models were selectedprimarily because they explicitly exclude crashes associated with intersections (both signalized andunsignalized). A fourth model that excludes only signalized intersection crashes is also included inthe summary. This model was added because it includes several factors included in the three othermodels and, thereby, provides some confirmation of the trends they exhibit.



Ci ' 0.000365 ADT L (Basei % Drive % Truck) AMFsw (1.0 & 0.01 PDOi) (4-1)

Harwood Models

The models described in this section are derived from the crash rates reported by Harwood(2) for suburban highways. The criteria used to identify a “suburban highway” were sufficientlybroad (e.g., speeds between 35 and 50 mph; signal spacing of 0.25 miles or more, etc.) that theresulting models are likely to reflect the safety experience of most urban streets with reasonableaccuracy. The reported crash rates are categorized by median type, number of through lanes, andadjacent land use. They are listed in Table 4-1.

Table 4-1. Base Crash Rates and Adjustment Factors Reported by Harwood (2).Base Crash Rate, crashes/million-veh-mi

Adjacent LandUse

Through Traffic Lanes and Median Type 1

2 Lanes 4 LanesUndivided TWLTL Undivided Raised Curb TWLTL

Commercial 2.39 1.56 2.85 2.90 2.69Residential 1.88 1.64 0.97 1.39 1.39

Adjustment FactorsDriveway density 2 Driveways/mile

crash rate adjustment factorUnder 30

-0.4130 to 60

-0.03Over 60+0.35

Truck presence Percent Truckscrash rate adjustment factor

Under 5+0.18

5 to 10-0.07

Over 10-0.33

Property-Damage-Only Crash Distribution, %Adjacent Land

UseThrough Traffic Lanes and Median Type 1

2 Lanes 4 LanesUndivided TWLTL Undivided Raised Curb TWLTL

Commercial 60.9 70.1 62.3 66.0 66.7Residential 57.8 56.3 62.0 55.2 60.4

Notes:1 - TWLTL - two-way left-turn lane.2 - Driveway density is based on a count of driveways on both sides of the street (i.e., a two-way total).

The rates in Table 4-1 can be used in the following equation to compute the expectedfrequency of severe crashes.

where:Ci = frequency of severe crashes on urban streets with median type and land use

combination i, crashes/yr;ADT = average daily traffic, veh/d;

L = street segment length, mi;Basei = base crash rate for urban street type i (see Table 4-1), crashes/million-veh-mi;

Drive = adjustment for driveway density (see Table 4-1), crashes/million-veh-mi;



Truck = adjustment for truck presence (see Table 4-1), crashes/million-veh-mi;AMFsw = shoulder width accident modification factor (1.05 if curb-and-gutter is used instead of

shoulder or if Ws is 4 ft or less; 0.95 if Ws more than 8 ft; 1.00 otherwise);Ws = outside shoulder width (paved or unpaved), ft; and

PDOi = percent property-damage-only crashes on urban streets of type i.

Equation 4-1 was developed using the guidance offered by Harwood (2). The adjustmentfactor for shoulder width in this equation was derived from the statement that “accident rates shouldbe decreased by 5 percent for highway sections with full shoulders and increased by 5 percent forhighway sections with no shoulders” (2, p. 9) where “full shoulders” is defined as shoulders of 8 ftor more and “no shoulders” is defined as shoulders of 4 ft or less. Given that the research includedcross sections both with and without curbs, it is inferred that the “no shoulders” case includes crosssections with curb and gutter.

The PDO term in Equation 4-1 was added to convert the total crash estimate into a severecrash estimate. The use of this adjustment is based on the assumption that the relationship betweenthe various model variables and total crash frequency is the same for severe crashes. The PDOpercentages needed for this adjustment are provided in Table 4-1.

The base crash rates in Table 4-1 for two-lane streets are consistent with the commonly heldbelief that the TWLTL is safer than an undivided cross section. However, the base crash rates forfour-lane streets do not maintain this consistency. They suggest that divided cross sections are lesssafe than undivided cross sections, a trend that is contrary to most research findings. Harwood (2)did not offer an explanation for these trends.

The characteristics of the data used by Harwood are summarized in Table 4-2. He used fiveyears of crash data from two states to compute the crash rates for three median types. All total, hisdatabase reflected the crash history of 420 suburban highway segments representing a total lengthof 254.8 miles.

Table 4-2. Database Characteristics for Various Safety Prediction Models.Model Developers Database Characteristics

Median Type Years ofCrash Data

Number ofStreet Segments



Harwood (2) Undivided 5 222 129.4 2, 4Raised curb 5 44 21.8 4

TWLTL 5 154 103.6 2, 4Hadi et al. (3) Undivided 4 not available not available 2, 6Hauer et al. (4) Undivided 4 not available 122.0 4Bonneson & McCoy (5) Undivided 3 62 26.0 2, 4

Raised curb 3 59 25.1 4, 6TWLTL 3 68 27.5 4, 5



CU,2 ' 0.25 ADT 0.9137 (1000 L)0.9330 e BU,2 (4-2)

BU,2 ' &11.415 & 0.0489(Wl % Wps) & 0.0201 V % 0.056 Ni & 0.0342 Wus (4-3)

CU,4 ' 0.25 ADT 0.8317 (1000 L)0.8831 e BU,4 (4-4)

BU,4 ' &9.584 & 0.1037 Wl & 0.0150 V % 0.0395 Ni & 0.3318 Icurb (4-5)

Hadi Models

The models described in this section are developed from the equations reported by Hadi etal. (3). They used negative binomial regression analysis to calibrate a set of safety predictionmodels. The models are categorized by crash severity, area type (i.e., urban, rural), number ofthrough lanes, and median type. Roads with a divided median were defined to include the followingmedian types: flush unpaved, raised curb, barrier median, and TWLTL.

In recognition of the varying influence of median type on crash frequency (as suggested bythe rates in Table 4-1), it was determined that only the Hadi models for undivided urban streets wereappropriate for inclusion in this chapter. These models are shown as Equations 4-2 and 4-4; theycan be used to compute the expected frequency of crashes on undivided two-lane and four-lanestreets, respectively.

with,

where:CU,2 = frequency of injury crashes on undivided two-lane urban streets, crashes/yr;

Wl = lane width, ft;Wps = paved shoulder width, ft;

V = speed limit, mph;Ni = number of intersections; and

Wus = unpaved shoulder width, ft.

with,

where:CU,4 = frequency of injury crashes on undivided four-lane urban streets, crashes/yr; andIcurb = presence of curb (1 if curb present, 0 otherwise).

The models developed by Hadi et al. (3) estimate injury crash frequency only; they do notinclude PDO or fatal crash frequency. Hadi et al. prepared separate models for estimating total crashfrequency and fatal crash frequency. Analysis of these models indicates that the estimates obtainedfrom Equations 4-2 and 4-4 should be inflated by 1 percent (i.e., multiplied by 1.01) to obtain anestimate of severe crash frequency.



C ' Coff&road % Con&road (4-6)

Coff&road ' 0.36 ADT10,000

0.815L e B % C (4-7)

C ' 0.230 (1 & Ipark) %320.9

R% 0.252 IV#30 % 0.318 IV$45 (4-9)

B ' &0.069 ADT10,000

% 0.148 Icurb % (1.0 & Icurb) ln(0.76 % 0.083 SWC ) & 0.184 Itwltl (4-8)

The sign of the constant associated with any single variable in the model’s linear terms (i.e.,those variables in Equations 4-3 and 4-5) indicates the correlation between a change in the variablevalue and crash frequency. For example, the negative sign of the constant associated with speedlimit V in either equation indicates that crash frequency is lower on roads with a higher speed limit.This trend is likely a reflection of the fact that higher speed roads are typically built to have moregenerous design element sizes and more forgiving roadside safety features.

The characteristics of the data used by Hadi et al. (3) are summarized in Table 4-2. Theyused four years of crash data to develop their safety prediction models. They did not report thenumber of road segments reflected in the database; however, the discussion suggests that it reflectsroad segments on the Florida state highway system.

Hauer Models

The models described in this section are developed from the equations reported by Hauer etal. (4). They used negative binomial regression analysis to develop safety prediction models forurban, four-lane undivided streets. These models are categorized by crash severity and crash location(i.e., off-the-road or on-the-road). The models, shown as Equations 4-6 through 4-12, can be usedto compute the expected frequency of severe crashes.

where:Coff-road = frequency of severe off-road crashes on undivided streets, crashes/yr; andCon-road = frequency of severe on-road crashes on undivided streets, crashes/yr.

The frequency of off-road crashes is computed using Equations 4-7 through 4-9. Theequation as published was intended to estimate crashes in one direction of travel. The constant“0.36” in Equation 4-7 has been increased by a factor of 2.0 over the value recommended by Haueret al. such that the estimated quantity reflects total crashes for both directions of travel.

with,

and,



Con&road ' 0.90 L ADT10,000

1.830A e B % 0.0205 Dd,b (4-10)

B ' &0.111 ADT10,000

% 0.113 Icurb % (1.0 & Icurb) ln(0.96 % 0.040 SWC ) & 0.229 Itwltl (4-11)

A '1

1502 e &0.059 Pt % 0.017 Pt e &2298/R %

343.8R

V 2.066 e &0.0689 V (4-12)

where:SWC = shoulder width category (1 if 0 to 1 ft, 2 if 2 to 3 ft, 3 if 4 to 6 ft, 4 if 7 to 9 ft, 5 if 10

to 11 ft, 6 if over 11 ft);R = curve radius, ft;

ln(x) = natural log of x;Itwltl = presence of two-way left-turn lane (1 if lane is present, 0 otherwise);Ipark = presence of on-street parking (1 if parking is present, 0 otherwise);IV#30 = low speed limit (1 if speed limit is 30 mph or less, 0 otherwise); andIV$45 = high speed limit (1 if speed limit is 45 mph or more, 0 otherwise).

The frequency of on-road crashes is computed using Equations 4-10 through 4-12. Theconstant “0.90” in Equation 4-10 has been increased by a factor of 2.0 over the value reported byHauer et al. such that the estimated quantity reflects total crashes for both directions of travel.

with,

and,

where:Dd, b = density of business or commercial driveways (two-way total), driveways/mi; and

Pt = percent trucks represented in ADT, %.

As with the previous models, the signs of the linear terms in Equations 4-8, 4-9, 4-11, and4-12 can be interpreted to indicate the change in crash frequency associated with a change in thecorresponding variable. An increase in the value of any variable with a positive coefficientcorresponds to an increase in crash frequency.

The characteristics of the data used by Hauer et al. (4) are summarized in Table 4-2.Specifically, they used four years of crash data from one state to develop their safety predictionmodels. Their database reflected the crash history for 122 miles of roadway.



C (

R ' ADT 0.910 (5280 L)0.852 e BR (1.0 & 0.01 PDO ) (4-13)

BR ' &15.162 & 0.296 Ib/o & 0.596 (1.0 & Ib/o ) % 0.00478 (Dd % Duia ) Ib/o % 0.0255 PDO (4-14)

BU,b/o ' &15.162 % 0.570 Ipark % 0.00478 (Dd % Duia ) % 0.0255 PDO (4-18)

C (

T ' ADT 0.910 (5280 L)0.852 e BT (1.0 & 0.01 PDO ) (4-15)

BT ' &15.162 % 0.018 Ib/o & 0.093 (1.0 & Ib/o) % 0.00478 (Dd % Duia ) Ib/o % 0.0255 PDO (4-16)

C (

U,b/o ' ADT 0.910 (5280 L)0.852 e BU, b/o (1.0 & 0.01 PDO ) (4-17)

Bonneson and McCoy Models

The models described in this section were developed from the equations reported byBonneson and McCoy (5). They used negative binomial regression analysis to develop models forestimating crash frequency for urban streets. These models differ from those previously describedbecause they yield the combined frequency of crashes that occur on the segment and at unsignalizedpublic street intersections. For this reason, the estimates obtained from these models are referred toherein as “mid-signal” crash frequencies.

Three models were developed by Bonneson and McCoy–one model for each of the followingmedian types: undivided, TWLTL, or raised curb. These models are shown as Equations 4-13through 4-20; they can be used to compute the expected frequency of severe mid-signal crashes.

with,

where:CR

* = frequency of severe, mid-signal crashes on urban streets with a raised-curb median,crashes/yr;

Ib/o = business or office land use (1 if business or office, 0 otherwise);Dd = driveway density (two-way total), driveways/mi;

Duia = unsignalized public street approach density (two-way total), approaches/mi; andPDO = property-damage-only crashes as a percentage of total crashes (= 68 percent).

with,

where:CT

* = frequency of severe, mid-signal crashes on urban streets with a TWLTL, crashes/yr.

with,



C (

U,r/i ' ADT 1.931 (5280 L)0.852 e BU, r/i (1.0 & 0.01 PDO ) (4-19)

BU,r/i ' &25.666 % 0.570 Ipark % 0.0255 PDO (4-20)

where:C*

U,b/o = frequency of severe, mid-signal crashes on undivided urban streets serving a businessor office land use, crashes/yr.

with,

where:C*

U,r/i = frequency of severe, mid-signal crashes on undivided urban streets serving residentialor industrial land use, crashes/yr.

The PDO terms in Equations 4-13, 4-15, 4-17, and 4-19 were added to convert the total crashestimate into a severe crash estimate. The data used by Bonneson and McCoy to calibrate theirmodel consisted of 68 percent PDO crashes. This factor should be used in the aforementionedequations to yield the desired severe crash frequency.

As with the previous models, the signs of the linear terms in Equations 4-14, 4-16, 4-18, and4-20 can be interpreted to indicate the change in crash frequency associated with a change in thecorresponding variable. An increase in the value of any variable with a positive coefficientcorresponds to an increase in crash frequency.

The characteristics of the data used by Bonneson and McCoy (5) are summarized inTable 4-2. Specifically, they used three years of crash data from cities in two states to develop theirsafety prediction models. Their database reflected the crash history for 189 street segments totaling78.6 miles.


The models described in the previous sections are compared in this section. The objectiveof this comparison is to determine which model or models are reasonable in their prediction ofsevere crash frequency. To facilitate this comparison, the models are examined over a range oftraffic volume levels. The models were grouped by median type and adjacent land use. The valuesof other model variables were set at typical values for urban streets. These values are listed inTable 4-3.



Table 4-3. Typical Values Used for Urban Street Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

Harwood(2)

Hadi et al.(3)

Hauer etal. (4)

Bonneson&McCoy (5)

Segment length, mi 0.5 U U U U

Driveway density,driveways/mile

50 for undivided50 for TWLTL

25 for raised curb

U -- U U

Number of intersections 5 -- U -- --Truck percentage 6.0 U -- U --Adjacent land use 1 varied U -- U U

Outside edge of pavement curb -- U U --Shoulder width, 2 ft 1.5 U U U --Lane width, ft 12 -- U -- --Curve radius, ft infinite (i.e., tangent) -- -- U --Presence of curb parking no -- -- U U

Presence of TWLTL varied U -- U U

Presence of median varied U -- -- U

Speed limit, mph 35 residential and industrial;40 business and office

-- U U --

Notes:1 - Land use categories: business (or commercial), office, industrial, and residential.2 - It is assumed that curb-and-gutter is provided on the typical urban street instead of a shoulder. This cross section

is assumed to have an equivalent “shoulder” width of 1.5 ft.

The expected crash frequencies obtained from the various models are shown in Figures 4-1,4-2, and 4-3. The model developer and land use adjacent to the street for a given trend line isindicated in each figure. Several trends can be seen in these figures. First, the figures indicate thatcrash frequency increases in a nearly linear manner with traffic volume. Second, streets inresidential areas typically experience fewer crashes than those in business (or commercial) areas.In this regard, there is a mild correlation between land use and driveway traffic demand, wheredriveways in business areas tend to have more traffic than those in residential areas.

When comparing across Figures 4-1, 4-2, and 4-3, the relationship between land use andcrash frequency can be seen to vary widely. This variability reflects the mild correlation betweenland use and driveway activity. Finally, there is a tendency for more crashes to occur on a four-lanestreet than a two-lane street for common land use and traffic volume. This trend is likely due to thefour-lane cross section’s increased exposure to adjacent-lane crashes.



0

1

2

3

4

0 5 10 15 20


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Commercial (Harwood)

Residential (Harwood)

Mix (Hadi et al.)

0.5 mile segment length

0

2

4

6

8

0 10 20 30 40


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr


Business/office (Bonneson & McCoy)

Commercial (Hauer et al.)

Mix (Hadi et al.)

Residential/indust. (B. & M.)



Residential (Hauer et al.)

0

1

2

3

4

0 5 10 15 20


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr




0

2

4

6

8

0 10 20 30 40


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr



Commercial (Hauer et al.)

Residential (Hauer et al.)



a. Two-Lane Streets. b. Four-Lane Streets.

Figure 4-1. Severe Crash Frequency for Undivided Streets.

a. Two-Lane Streets. b. Four-Lane Streets.

Figure 4-2. Severe Crash Frequency for Streets with TWLTL.

The correlation between median type and crash frequency was evaluated by examination ofall the models shown in Figure 4-2. For a common volume, land use, and lanes, streets with a raised-curb median consistently have fewer severe crashes than those with undivided cross sections. Incontrast, crash frequencies for undivided streets and those with a TWLTL are fairly similar. If anoverall average of the trend lines is taken, a street in a business or commercial area with a TWLTLmay experience a slightly lower crash frequency than an undivided street in the same area. Thesetrends do not extend to streets with a TWLTL that are located in residential areas. They are likelya reflection of the significant amount of driveway activity that occurs in business or commercialareas (relative to residential areas) and the fact that the TWLTL provides storage for turning vehicles.

The models listed in Table 4-3 estimate the frequency of crashes that involve at least onevehicle. Hence, the estimate obtained includes crashes involving pedestrians or bicycles withautomobiles, trucks, or buses. Given that these crashes represent a relatively small portion of thetotal number of crashes, it is likely that AMFs derived from these models do not accurately reflectthe relationship between a design element and the frequency of pedestrian or bicycle-related crashes.



0

2

4

6

8

0 10 20 30 40


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr



Residential/indust. (B. & M.)Residential (Harwood)


Figure 4-3. Severe Crash Frequency for Four-Lane Streets with Raised-Curb Median.


This part of the chapter describes various accident modification factors that are related to thedesign of an urban street. The various factors examined are organized into the following categories:roadway geometric design, roadside design, and access control.

Geometric Design

This section describes AMFs related to the geometric design of an urban street. Topicsspecifically addressed are listed in Table 4-4. Many geometric design components or elements arenot listed in this table (e.g., grade) that are also likely to have some correlation with severe crashfrequency. However, a review of the literature did not reveal useful quantitative informationdescribing these effects. The list of available AMFs for urban street geometric design is likely toincrease as new research in this area is undertaken.

Table 4-4. AMFs Related to Geometric Design of Urban Streets.Section Accident Modification Factor

Horizontal alignment Horizontal curve radiusCross section Lane width Shoulder width Median width

TWLTL median type Curb parking Uncurbed cross section

In some instances, an AMF is derived from a safety prediction model as the ratio of “segmentcrash frequency with a changed condition” to “segment crash frequency without the change.” Inother instances, the AMF is obtained directly from a before-after study. Occasionally, crash ratesreported in the literature were used to derive an AMF.



AMFcr ' 2.30 e &2298/R %343.8

R[1&Poff&road] % 0.781 (e 320.9 /R ) Poff&road (4-21)

0.6

0.8

1.0

1.2

1.4

1.6

500 700 900 1100 1300 1500 1700 1900

Curve Radius, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 4-Lane, Undivided (modified Hauer et al. [4])

Derived



This subsection describes AMFs related to the urban street’s horizontal alignment. The onlyhorizontal alignment AMF found in the literature applies to horizontal curve radius for undividedurban streets. This AMF was derived from the safety prediction model developed by Hauer et al.(4). It is shown as Equation 4-21 and reflects one modification from the original model form.Specifically, the constants “2.30” and “0.781” are added for the reasons offered in the nextparagraph. The use of Equation 4-21 requires knowledge of the proportion of off-road crashes. Thecrash data analyzed by Hauer et al. reflect a proportion of off-road crashes equal to 0.14.

where:AMFcr = curve radius accident modification factor; andPoff-road = proportion of crashes that occur off the roadway.

The structure of Hauer’s original equation is such that the use of a tangent as the basecondition yields AMF values of less than 1.0 for curved segments, which is illogical. Equation 4-21represents a modified version of the original equation. The modification reflects the use of a 1300 ftbase condition such that AMF values equal 1.0 or more for all radii. The constants “2.30” and“0.781” were added to Equation 4-21 to reflect this modification. This relationship is shown inFigure 4-4 for a proportion of off-road crashes Poff-road equal to 0.14.

Figure 4-4. Curve Radius AMF for Urban Streets.




Pb

% 1.0 (4-23)

AMFlw,b ' e &0.040 (Wl & 12) (4-22)

AMFlw, i ' (e &0.040 (Wl & 12)& 1.0)

Pi

0.24% 1.0 (4-24)

For radii less than 1300 ft, Equation 4-21 is consistent with AMFs for rural highways in thatcrash frequency increases with decreasing radii. However, for radii larger than 1300 ft, it suggeststhat crash frequency increases as radius increases. This increase is not consistent with rural highwayAMFs and additional research is needed to determine if it is true. Until then, Equation 4-21 isrecommended for radii less than 1300 ft, and an AMF of 1.0 is recommended for larger radii. Therecommended AMF is shown in Figure 4-4 as the thick bold line labeled “derived.”

Cross Section

Lane Width. A relationship between lane width and crash frequency was derived from thesafety prediction models developed by several researchers. This derivation is described in theGeometric Design section of Chapter 3. When applied to urban streets, the following equation wasdeveloped for computing the lane width AMF for the base combination of lanes and median type(i.e., four-lane, raised-curb median street). The base condition lane width for this AMF is 12 ft.


type (i.e., four-lane, raised-curb median street).

Equation 4-22 can be combined with the following equation to obtain the lane width AMFfor other combinations of lanes and median type.




The values of Pi and Pb correspond to the crashes influenced by the AMF, and are both representedas a proportion of all crashes. The crash distribution used for Pi is that reflecting the crash historyof the roadway type corresponding to bi. The distribution used for Pb is that reflecting a specifiedbase combination of lanes and median type. For this analysis, a street with a four-lane, raised-curbmedian street was chosen to represent the base combination. The proportion of influential crashesfor the base combination Pb is 0.24.

The AMF that results from the combination of Equations 4-22 and 4-23 is:

It can be tailored to a desired number of lanes and median type by using the variable Pi. Values forthis variable are listed in Table 4-5. The proportions in this table (and subsequent similar tables)



0.8

1.0

1.2

1.4

1.6

1.8

9 9.5 10 10.5 11 11.5 12

Lane Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 2-Lane, Undivided (derived)

Urban, 4-Lane, Undivided (Hadi et al. [3])

Urban, 2-Lane, Undivided (Hadi et al. [3])


AMFsw,b ' e &0.014 (Ws & 1.5) (4-25)

were obtained from the crash database maintained by the State of Texas, Department of PublicSafety.

Table 4-5. Crash Distribution for Urban Street Lane Width AMF.Area Type Median Type Crash Type Subset Through Lanes Subset ProportionUrban Undivided or

TWLTLSingle-vehicle run-off-road, either side

same direction sideswipe, multiple vehicle opposite direction

2 0.254 0.186 0.14

Raised curb Single-vehicle run-off-road, either sidesame direction sideswipe

4 0.246 0.27

The AMFs obtained from Equation 4-24 are illustrated in Figure 4-5. They are labeled“derived” and have a bold line weight. They are compared to the AMFs developed by otherresearchers. The trend is one of increasing AMF value with a reduction in lane width. For a givenlane width, the derived AMF for two-lane streets is larger than that for four-lane streets. There isgeneral agreement between the derived AMFs and those reported in the literature. Significantdifferences between AMFs are likely a reflection of bias (due to colinearity) in the original models.

Figure 4-5. Lane Width AMF for Urban Streets.

Shoulder Width. The following equation represents the shoulder width AMF for the basecombination of lanes and median type (i.e., four-lane, raised-curb median street). It was derived ina similar manner as the lane width AMF (as described in Chapter 3). The base condition shoulderwidth is 1.5 ft.



AMFsw, i ' ( e &0.014 (Ws & 1.5)& 1.0)

Pi

0.088% 1.0 (4-26)

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10

Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 2-Lane, Univided (Hadi et al.[3])

Suburban, 2 & 4-Lane (Harwood [2])


where:AMFsw, b = shoulder width accident modification factor for the base combination of lanes and

median type (i.e., four-lane, raised-curb median street); andWs = shoulder width, ft.

Equation 4-25 can be combined with Equation 4-23 to obtain the shoulder width AMF forother combinations of lanes and median type. The proportion of influential crashes for the basecombination Pb is 0.088. The resulting AMF is:


Table 4-6. Crash Distribution for Urban Street Shoulder Width AMF.Area Type Median Type Crash Type Subset Through Lanes Subset ProportionUrban Undivided or

TWLTLSingle-vehicle run-off-road, either side 2 0.17

4 0.106 0.054

Raised curb Single-vehicle run-off-road, right side 4 0.0886 0.087

The AMFs obtained from Equation 4-26 are illustrated in Figures 4-6 and 4-7. They arelabeled “derived” and have a bold line weight. They are compared to the AMFs developed by otherresearchers.

Figure 4-6. Shoulder Width AMF for Two-Lane Urban Streets.



AMFmw 'b0 (e b1 W

b2m & 1.0) % 1.0

b0 (e b1 16b2

& 1.0) % 1.0(4-27)

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10

Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 4-Lane, Undivided (Hauer et al. [4])

Suburban, 2 & 4-Lane (Harwood [2])

Urban, 4-Lane (derived)

Urban, 4-Lane, Divided (Hadi et al.[3])

Figure 4-7. Shoulder Width AMF for Four-Lane Urban Streets.

The Harwood (2) AMF was derived from Equation 4-1. Values for this AMF vary byshoulder width as follows: 1.0 for 0 to 4 ft, 0.95 for 5 to 7 ft, 0.90 for 8 ft or more. The AMFextracted from the Hauer et al. (4) model was derived from Equations 4-8 and 4-11. Values for thisAMF vary by shoulder width as follows: 1.0 for 2 to 3 ft; 1.05 for 4 to 6 ft; 1.09 for 7 to 9 ft; and1.14 for 10 to 11 ft.

With one exception, the trends in Figures 4-6 and 4-7 show a decreasing AMF value withan increase in shoulder width. For a given shoulder width, the AMF for two-lane streets is smallerthan that for four-lane streets. There is general agreement between the derived AMFs and thosereported in the literature. The one exception is the AMF developed by Hauer et al. (4) for four-lanestreets. It suggests that wider shoulders are associated with increased crashes which is contrary tocommon belief. It is likely that this trend is indirectly a result of a negative correlation betweenshoulder width and other variables that were not included in the safety prediction model.

Median Width. AMFs for median width were developed from safety prediction modelsdeveloped by Hadi et al. (3) and Bowman et al. (6). All AMFs are based on models developed forurban, four-lane and six-lane, divided streets. Equation 4-27 was developed to represent these twoAMFs. The base condition for this AMF is a 16 ft median width. The coefficients used in the modelare listed in columns 4 through 6 of Table 4-7.

where:AMFmw = median width accident modification factor; and




0.6

0.8

1.0

1.2

1.4

1.6

5 10 15 20 25 30

Median Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

6-Lane (Hadi et al.[3])

4-Lane (Hadi et al.[3])

Derived

4 & 6-Lane (Bowman et al.[6])

Table 4-7. Coefficient Values for Median Width on Urban Streets.Model Source Roadway Type Crash


Coefficientsb0 b1 b2Hadi et al. (3) Urban, 4-lane, divided Injury 1.0 -0.0325 0.5 -0.0325

Urban, 6-lane, divided Injury 1.0 -0.0501 0.5 -0.0501Bowman et al. (6) Urban, 4 & 6-lane, divided All 1.0 -0.0275 1.0 -0.2008

Weighted Average: -0.041

Figure 4-8 illustrates the AMFs listed in Table 4-7. The two AMFs attributed to Hadi et al.(3) are in good agreement. They are also in good agreement with the median width AMF derivedfor rural highways (see Chapter 3). The AMF derived from the Bowman et al. (6) model is in lessagreement and indicates a much greater sensitivity to median width.

Figure 4-8. Median Width AMF for Urban Streets.

The derived AMF relationship is shown in Figure 4-8. It is based on Equation 4-27 with b0= 1.0, b2 = 0.5, and the weighted average of the equivalent b1 coefficients listed in columns 7 and 8of Table 4-7 (where the weight w for each coefficient is equal to its reciprocal squared [i.e., w =1/b2]). The equivalent b1 coefficient for the Bowman AMF was derived from a regression analysisusing Equation 4-27 with b0 = 1.0 and b2 = 0.5 for median widths ranging from 5 to 30 ft. The AMFsobtained from Equation 4-27 (using the base coefficients) served as the dependent variable.

TWLTL Median Type. As noted in the discussion of Figures 4-1 and 4-2, the differencebetween a street with a TWLTL and an undivided street is not readily apparent in terms of theirexpected crash frequency for a given traffic volume and land use. This lack of a clear difference islikely due partly to differences in driveway traffic activity. Harwood et al. (7) developed an AMF



AMFT ' 1.0 & AMFtarget PD PLT/D (4-28)

Ptarget ' 1 & e &0.008 Dd,b/o (nl % 1) (4-31)

PD '0.0047 Dd % 0.0024 D 2

d

1.199 % 0.0047 Dd % 0.0024 D 2d

(4-29)

AMFT ' (AMFtarget & 1.0) Ptarget % 1.0 (4-30)

to capture this effect as it relates to the addition of a TWLTL to a two-lane rural highway. This AMFis shown as Equation 4-28.

with,

where:AMFT = TWLTL accident modification factor;

AMFtarget = AMF for crash types directly influenced by the addition of a TWLTL (= 0.70);PD = driveway-related crashes as a proportion of total crashes; and

PLT/D = left-turn accidents susceptible to correction by a TWLTL as a proportion of driveway-related crashes (estimated as 0.50).

The effectiveness of the TWLTL, when added to an undivided street, has been researchedby many individuals. In their review of previously conducted before-after studies, Bonneson andMcCoy (5) noted that crash reduction factors associated with the TWLTL ranged from 28 to44 percent (i.e., AMFs of 0.56 to 0.72). The AMFs for target crashes (i.e., left-turn, rear end, etc.)were found to vary from 0.53 to 0.67. One of the reports they reviewed was a before-after studyconducted by Thakkar (8). His database included information for 15 sites that had four through lanesand 16 sites that had two through lanes. However, 11 of the four-through-lane sites and four of thetwo-through-lane sites were selected for conversion because they were high-accident locations(HALs). Table 4-8 lists the data reported by Thakkar for the sites that were not HALs.

The AMFs listed in Table 4-8 suggest that a TWLTL has a smaller safety benefit (i.e., largerAMF) when applied to a street with two through lanes than when applied to a street with fourthrough lanes. They also confirm that certain crash types (i.e., left-turn, rear end, and sideswipe) aremore likely to be reduced by a TWLTL than other crash types (e.g., fixed object).

Equation 4-30 was derived to combine the concepts expressed in Equation 4-28 with theAMFs listed in Table 4-8. Equation 4-31 is used to estimate the proportion of target crashes Ptarget.

with,

where:Ptarget = target crashes as a proportion of total crashes;

nl = number of through lanes; andDd, b/o = density of driveways serving business or office land uses (two-way total),

driveways/mi.



Table 4-8. Before-After TWLTL Crash Data Analysis.Site Thru.

LanesADT Total Crashes Target Crashes

Before After Before After Predicted Before After Predicted4 4 12,300 13,500 116 58 127.3 30 11 32.97 4 15,000 15,000 52 42 52.0 13 3 13.011 4 23,000 22,000 116 56 111.0 46 30 44.012 4 23,000 24,200 66 89 69.4 17 24 17.9

Total: 245 359.7 Total: 68 107.8AMFT: 0.68 AMFtarget: 0.63

1 2 4200 3800 4 0 3.6 3 0 2.72 2 6900 6900 15 11 15.0 2 1 2.03 2 8200 8550 48 43 50.0 13 11 13.64 2 8400 8500 9 5 9.1 3 2 3.05 2 8500 9200 14 4 15.2 13 3 14.16 2 8550 8600 7 6 7.0 3 4 3.07 2 10,000 11,050 27 23 29.8 18 11 19.98 2 10,600 11,500 8 13 8.7 2 4 2.29 2 10,700 10,900 19 18 19.4 0 1 0.0

11 2 11,700 10,300 45 52 39.6 7 10 6.213 2 15,900 16,700 108 109 113.4 29 29 30.514 2 16,150 16,700 52 35 53.8 21 13 21.7

Total: 319 364.7 Total: 89 118.8AMFT: 0.87 AMFtarget: 0.75

As in Equation 4-29, the driveway density term is included in Equation 4-31 to reflect thecorrelation between driveway density and the distribution of crashes. The number-of-lanes term isincluded for similar reasons. Logically, a wider cross section is likely to be correlated with anincrease in target crashes. The Pb/o term is included because an analysis of driveway influence (seethe section titled Access Control) indicated that driveways associated with a residential land use donot have a significant correlation with crash frequency. The constant “-0.008” represents a best-fitcalibration coefficient that was derived using the AMFs in Table 4-8 and an estimated averagedriveway density of 30 and 50 driveways/mi for the two-lane and four-lane cross sections,respectively. These average densities were obtained from the report by Harwood (2).

The AMF for adding a TWLTL to an urban street is shown in Figure 4-9. The trend lineattributed to Harwood et al. (7) is based on Equations 4-28 and 4-29. It indicates that the TWLTLis more effective at reducing crashes as driveway density increases. The thick trend lines are basedon Equations 4-30 and 4-31. A similar trend with driveway density is reflected in these equations.



0.4

0.6

0.8

1.0

1.2

1.4

0 20 40 60 80 100


Acc

iden

t Mod

ifica

tion

Fact

orUrban, 2-Lane (derived)

Rural, 2-Lane (Harwood et al.[7])

Urban, 4-Lane (derived)

Figure 4-9. TWLTL Median Type AMF for Urban Streets.

Curb Parking. AMFs for curb parking were developed from the safety prediction modeldeveloped by Bonneson and McCoy (5) and from data reported by McCoy et al. (9). The safetyprediction model was described previously. The AMF from the McCoy data was developed for thischapter. McCoy et al. examined the relationship between number of through lanes, adjacent landuse, and crash frequency on urban streets in Nebraska. The crash frequencies they reported forstreets with parallel parking are provided in Table 4-9. The corresponding AMFs for parallel parkingare shown in the last column of the table.

Table 4-9. AMFs for Parallel Parking on Urban Streets.Data Source Through

LanesPercent Business orOffice Land Use 1

Crash Frequency by Type AMFpp 2

Parallel Parking TotalBonneson & McCoy (5) 4 100 not available not available 1.77McCoy et al. (9) 2 75 19 41 1.86

20 51 130 1.65>2 69 66 198 1.50

35 66 307 1.27Notes:1 - “Business or Office Land Use” is defined to include retail, service, office, and medical facilities.2 - AMF for Bonneson & McCoy (5) was computed as e0.57. For the other data source, it is computed as total/(total!

parallel parking).

The data in Table 4-9 indicate that there is a relationship between land use, through lanes,and the parallel parking AMF. This relationship is shown in Figure 4-10. The AMFs in the lastcolumn of Table 4-9 are shown as data points. The trends indicate that crash frequency increases



AMFpk ' 1 % Ppk (Bpk & 1) (4-32)

1.0

1.2

1.4

1.6

1.8

2.0

0 20 40 60 80 100

Business or Office Land Use, %

Acc

iden

t Mod

ifica

tion

Fact

or:Undivided two-lane:Multilane

Bpk ' (1.10 % 0.365 Iu2 % 0.609 Pb/o ) [( fap/pp & 1.0) Pap % 1.0] (4-33)

linearly with the percentage of business or office land use. Crashes are also more frequent on two-lane streets than multilane streets.

Figure 4-10. Parking AMF for Urban Streets.

The “business or office” land use percentages in Table 4-9 for McCoy et al. (9) reflect thepercentage of painted stalls at each study site. The locations with a low percentage of business oroffice use almost always had unpainted parking stalls. Those locations with a high percentage ofbusiness or office land use almost always had painted stalls. Regardless, the variation among AMFsin Table 4-9 is more likely correlated with land use, and associated parking activity, than whetherthe stall was painted.

Box (10) recently reviewed several studies that contrasted angle parking with parallelparking. He concluded that streets with angle parking had crash rates that were 1.5 to 3 times largerthan those streets with parallel parking. Some of the data he used to form this conclusion aresummarized in Table 4-10.

Based on the trends described in the preceding paragraphs, the following AMF was derivedto reflect the correlation between curb parking and crash frequency. The base condition for thisAMF is “no parking.”

where:AMFpk = parking presence accident modification factor;

Ppk = proportion of street segment length with parallel or angle parking (= 0.5 Lpk / L);



AMFno curb ' (e b ( Icurb & 1)& 1.0) Ps % 1.0 (4-34)

Lpk = curb miles allocated to parking, mi;Iu2 = indicator variable for cross section (1 for two-lane street; 0 otherwise);

Pb/o = for that part of the street with parking, the proportion that has business or office as anadjacent land use;

fap/pp = ratio of crashes on streets with angle parking to those on streets with parallel parking(see Table 4-10); and

Pap = for that part of the street with parking, the proportion with angle parking.

Table 4-10. Comparison of Angle Parking with Parallel Parking.Data Source Roadway Type Parking Crash Rate Units fang/pp

Angle CrashRate

Parallel CrashRate

Box (10) Table 6

Collector 211 84 parking crash/mi 2.51Local 147 56 parking crash/mi 2.63

Box (10)Table 9

Retail 15.0 7.5 crash/mi 2.00Retail/mixed 9.9 5.4 crash/mi 1.83Residential 5.3 1.9 crash/mi 2.79

Box (10)Table 10

Collector 13.5 9.4 crash/mi 1.44Local 14.6 4.8 crash/mi 3.04

McCoy et al. (9)Tables 12 & 13

Painted stalls 14.4 5.0 crash/bvmh/stall 1 2.88Unpainted stalls 5.4 2.8 crash/bvmh/stall 1 1.93

Average: 2.34Note:1 - Crashes per 10 billion vehicle-mile-hours/stall.

Uncurbed Cross Section. The relationship between the presence of an outside curb andcrash frequency was derived from models developed by Hadi et al. (3) and by Hauer et al. (4). Inaddition to the models shown as Equations 4-2 and 4-4, Hadi et al. (3) developed models forestimating: (1) total crash frequency for two-lane and four-lane undivided streets, (2) total crashfrequency for six-lane divided streets, and (3) injury crash frequency for six-lane divided streets.Each of these models included an indicator variable for curb presence. The AMFs extracted fromthe urban, four-lane, undivided models indicated that crashes would be higher on an uncurbed crosssection. This trend is illogical and likely the result of some correlation among model variables. ThisAMF was not considered further. The AMFs extracted from the remaining Hadi models arerepresented by Equation 4-34, in combination with Table 4-11.

where:AMFno curb = uncurbed cross section accident modification factor, and

Icurb = presence of curb (1 if curb present, 0 otherwise).



AMFno curb ' e bon road ( Icurb & 1) (1 & Ps) % e boff road ( Icurb & 1) Ps (4-35)

Table 4-11. Coefficient Values for Uncurbed Cross Section on Urban Streets.Model Source Roadway Type Crash


Crash TypesSubset Pro-portion, Ps

Coefficientb

AMF

Hadi et al. (3) Urban, 2-lane, undivided All All 1.0 0.1707 0.84Urban, 6-lane, divided Injury All 1.0 0.2202 0.80

All All 1.0 0.1671 0.85Hauer et al. (4) Urban, 4-lane, undivided Injury Off-road crashes 0.14 0.225 1 0.91

On-road crashes -- 0.074 1

All Off-road crashes 0.14 0.291 2 0.86On-road crashes -- 0.132 2

Notes:1 - Values listed are derived from Equations 4-8 and 4-11 using a curb as the base condition and a flush shoulder of 2

to 3 ft representing the no curb condition (i.e., SWC = 2) (e.g., 0.225 = ln(1.16) - ln[0.76 + 0.083 × SWC]).2 - Values listed are derived from equations reported by Hauer et al. (4).

The models presented by Hauer et al. were used to develop the following equation forestimating an uncurbed cross section AMF. The equation coefficients and subset proportions arelisted in Table 4-11.

Column 4 of Table 4-12 lists AMFs that are computed using the coefficients and subsetproportions listed in Table 4-11. Equation 4-34 was used with the Hadi coefficients and proportions.Equation 4-35 was used with the Hauer coefficients and proportions. The AMF values are in generalagreement and range from 0.80 to 0.91.

Table 4-12. AMFs for Uncurbed Cross Section on Urban Streets.Model Source Roadway Type Crash

SeverityAMFs fromTable 4-11 1

Subset Pro-portion, Ps 2

AMFs fromEqu. 4-35 3

Hadi et al. (3) Urban, 2-lane, undivided Injury not available 0.17 0.91All 0.84 0.85

Hauer et al. (4) Urban, 4-lane, undivided Injury 0.91 0.10 0.92All 0.86 0.86

Hadi et al. (3) Urban, 6-lane, divided Injury 0.80 0.17 0.91All 0.85 0.85

Notes:1 - AMFs are computed using the coefficients and subset proportions listed in Table 4-11 with the corresponding

equation (i.e., Equation 4-34 or 4-35).2 - Proportions are obtained from Table 4-6 and represent single vehicle run-off-road crashes in Texas.3 - AMFs are computed using Equation 4-35 with the subset proportions in column 5 and the coefficients (in Table 4-

11) from the Hauer model.



AMFno curb ' e &0.074 (1 & Poff&road) % e &0.225 Poff&road (4-36)

The subset distribution of run-off-road crashes listed in Table 4-6 was used to facilitatecomparison of the Hauer coefficients with those from the Hadi models. Specifically, this distributionwas used with Equation 4-35 and Hauer’s coefficients, to estimate the AMFs in the last column ofTable 4-12. The AMFs shown in this column compare favorably with those obtained from the Hadimodels. This finding suggests that there is general agreement among the AMF model sources on thecorrelation between curb exclusion and crash frequency—provided that differences in median typeand number-of-lanes are accounted for using the appropriate subset crash proportions. Thus, thefollowing equation is rationalized to offer a reasonable method for estimating the uncurbed crosssection AMF for urban streets:

The proportion of off-road crashes Poff-road is obtained from Table 4-6.

Roadside Design

This section describes AMFs related to the roadside design of an urban street. Topicsspecifically addressed are listed in Table 4-13. Many roadside design components or elements thatare not listed in this table (e.g., ditch shape) are also likely to have some correlation with crashfrequency on the urban street segment. However, a review of the literature did not reveal that theireffect has been quantified by previous research. The list of available AMFs for urban street roadsidedesign is likely to increase as new research in this area is undertaken.

Table 4-13. AMFs Related to Roadside Design of Urban Streets.Section Accident Modification Factor

Cross section Utility pole offsetAppurtenances see text


Cross Section

This subsection is devoted to the presentation of AMFs related to the roadside cross sectionof an urban street. A review of the literature indicates that horizontal clearance, side slope, utilitypole offset, and bridge width may have some influence on crash frequency. However, with one



AMFpd ' (fp & 1.0) Ps % 1.0 (4-37)

fp '(0.0000984 ADT % 0.0354 Dp ) W &0.6

o & 0.040.0000649 ADT % 1.128

(4-38)

exception, these correlations have not been quantified for urban streets. Rather, the focus ofprevious research has been on rural, two-lane highways. The one exception is utility pole offset.This research included crashes on urban roadways in the database. This subsection describes anAMF for utility pole offset and “density” (where pole density relates to pole frequency per unitlength of roadway).

The correlation between utility pole offset, pole density, and crash frequency was evaluatedby Zegeer and Parker (12). They developed a safety prediction model using data from four states.The model included average pole offset, traffic volume, and pole density as independent variables.The AMF derived from this model is described in Equation 4-37. Details of the model are describedin Table 4-14. The base condition is 50 poles/mi and a pole offset of 2.0 ft.

with,



Table 4-14. Coefficient Values for Utility Pole Offset on Urban Streets.Model Source Roadway Type Crash

SeveritySubset of



The subset proportions appropriate for Texas urban street applications are provided inTable 4-15. Equation 4-37 yields an AMF that ranges from 1.02 at a pole density of 90 poles/mi andoffset of 2.0 ft to 0.96 at a pole density of 20 poles/mi and offset of 30 ft. The AMF is moresensitive to pole offset than it is to density or average daily traffic volume.

Table 4-15. Crash Distribution for Urban Street Utility Pole Offset AMF.AreaType

MedianType

Crash Type Subset Through Lanes Subset Proportion

Urban Undivided orTWLTL

Single-vehicle collision with pole 2 0.0424 0.0366 0.017

Raised curb Single-vehicle collision with pole 4 0.0456 0.046



Appurtenances

As discussed previously, AMFs for roadside safety appurtenances are not described in thischapter. The safety literature related to roadside appurtenances has focused on the informationneeded to evaluate the cost-effectiveness of installing individual appurtenances at specific locations.Most of the research conducted in this area has been incorporated into a complex and comprehensiveprocedure for evaluating appurtenances on a case-by-case basis. This procedure is outlined in areport by Mak and Sicking (13) and automated in the Roadside Safety Analysis Program (RSAP)(14).

RSAP can be used to evaluate alternative roadside safety appurtenances on individual streetsegments. The program accepts as input information about the street segment geometry and trafficcharacteristics. It also allows the analyst to describe the roadside cross section, location of fixedobjects, and safety appurtenance design. Table 4-16 summarizes the various RSAP inputs. Theoutput from RSAP includes an estimate of annual crash frequency as well as the road-user costsassociated with these crashes. The crash reduction potential realized by adding a roadside safetyappurtenance (or changing the roadside cross section) can be estimated by specifying the changedcondition as an “alternative.”





-- Traffic volume (ADT) Truck presenceTraffic growth factor

Geometricdesign



Roadsidedesign






AMFdd ' e 0.0105 (Dd & Dbase ) (4-41)

AMFdd ' e 0.008 (Dd,b/o & 50) (4-42)

AMFdd ' 1.0 %DriveBasei

(4-40)

AMFdd ' e 0.00478 (Dd & Dbase ) (4-39)

Access Control

This section is devoted to AMFs related to the access control elements of an urban street.A review of the literature indicates that median type, adjacent land use (as a surrogate for drivewayactivity), and driveway density have an influence on crash frequency. The correlation betweenmedian type and crashes is addressed previously in the sections titled Safety Prediction Models andTWLTL Median Type. The correlation between land use and crashes is also addressed in the parttitled Safety Prediction Models. This section on access control describes the correlation betweendriveway density and crash frequency.

Three accident modification factors for driveway density were identified during the literaturereview. The first AMF for driveway density was derived from the Bonneson and McCoy modeldescribed previously. It is based on driveways in business or office areas. The form of this AMF is:

where:AMFdd = driveway density accident modification factor; and

Dbase = base driveway density, driveways/mi.

A second AMF was derived from the crash rates developed by Harwood (2). These rateswere reported previously in Table 4-1. Trends in the driveway density adjustment factors suggestthat they reflect a base condition of about 50 driveways/mi. The AMF was computed from the ratesin Table 4-1 as:

A third AMF for driveway density was derived from a model developed by Sawalha andSayed (15). It is based on driveways in business areas. The form of this AMF is:

The three AMFs are compared in Figure 4-11 for a base driveway density of50 driveways/mi. The trends in the data indicate that the relationship between driveway density andcrashes varies widely. This variation is likely due to the fact that driveway activity level (i.e., trafficdemand) is not used in the models. A surrogate for this activity is land use such that driveways inbusiness and office areas are likely to have significant traffic activity as to be associated withfrequent driveway-related crashes. In contrast, driveways in residential and office areas tend to haverelatively low volume and a corresponding minimal association with crash frequency.

A best-fit AMF for driveway density was derived from the relationships shown in Figure 4-11. The form of this AMF is:

where:Dd, b/o = density of driveways serving business or office land uses, driveways/mi.



AMFtk ' (ftk & 1.0) (1 & Poff&road) % 1.0 (4-43)

ftk '2 e &0.059 Pt % 0.017 Pt

1.506(4-44)

0.6

0.8

1.0

1.2

1.4

1.6

0 20 40 60 80 100


Acc

iden

t Mod

ifica

tion

Fact

orUrban, Business/Office (Bonneson & McCoy[5])

Urban, Commercial(Harwood [2])

Urban, Business(Sawalha & Sayed [15])

Derived

Figure 4-11. Driveway Density AMF for Urban Streets.


This section describes AMFs related to features of the street that are not categorized asrelated to geometric design, roadside design, or access control. Specifically, the AMFs describedin this section address truck presence and speed limit.

Truck Presence

AMFs for truck presence were derived from the Hauer and the Harwood safety predictionmodels. The AMF derived from the Hauer model is shown in Equation 4-43. It reflects a base truckpercentage of 6.0 percent. The proportion of off-road crashes in the database used by Hauer et al.is 0.14.

with,

where:AMFtk = truck presence accident modification factor; and Poff-road = proportion of crashes that occur off the roadway.

An AMF was also developed from the Harwood model using the rates reported previouslyin Table 4-1. Trends in this truck presence adjustment factor suggest that it reflects a base conditionof about 6.0 percent. The AMF computed from the rates in Table 4-1 is:



AMFtk ' 1.0 %TruckBasei

(4-45)

0.6

0.8

1.0

1.2

1.4

1.6

0 5 10 15 20

Truck Percentage, %

Acc

iden

t Mod

ifica

tion

Fact

or

Divided and Undivided(based on Harwood [2])

Undivided (based on Hauer et al.[4])

AMFsl ' e (0.252 IV#30 % 0.318 IV$45) Poff&road % 1.15 V 2.066 e &0.0689 V (1 & Poff&road) (4-46)

AMFsl ' e b (V & 40) (4-47)

The two AMFs described above are compared in Figure 4-12 for a range of truck percentages.The trends in the data indicate that increasing truck percentage is associated with fewer crashes. Itis likely that an increase in trucks does not make the street safer; rather, it probably indicates thatdrivers are more cautious when there are many trucks in the traffic stream.

Figure 4-12. Truck Presence AMF for Urban Streets.

Speed Limit

AMFs for speed limit were derived from the Hauer and the Hadi safety prediction models.The AMF from the Hauer model is shown as Equation 4-46. It reflects a base speed limit of 40 mph.The proportion of off-road crashes in the database used by Hauer et al. is 0.14.

where:AMFsl = speed limit accident modification factor.

An AMF for speed limit was also derived from the Hadi model. It is shown in Equation 4-47for a base speed limit of 40 mph. The value of each coefficient b is provided in Table 4-17.



0.4

0.6

0.8

1.0

1.2

1.4

30 35 40 45 50 55 60

Speed Limit, mph

Acc

iden

t Mod

ifica

tion

Fact

or

Urban, 2-Lane, Undivided (Hadi et al.[3])

Urban, 4-Lane, Undivided (Hadi et al.[3])

Urban, 4-Lane, Divided (Hadi et al.[3])

Urban, 4-Lane, Undivided (Hauer et al.[4])

Table 4-17. Coefficient Values for Speed Limit for Urban Streets.Model Source Roadway Type Crash

SeveritySubset of

Influenced Crash TypesCoefficient b

Hadi et al. (3) Urban, 2-lane, undivided Injury All -0.0201Urban, 4-lane, undivided Injury All -0.0155Urban, 4-lane, divided Injury All -0.0295

The two AMFs are compared in Figure 4-13. The trends in the data indicate that higherspeed limits are associated with fewer severe crashes. Although not shown in the figure, a similartrend was found by Bowman et al. (6). It is likely that an increase in speed limit does not make thestreet safer; rather, it probably indicates that streets with a higher speed limit tend to have a moregenerous design. Moreover, if just vehicle-pedestrian crashes were evaluated, their frequency wouldlikely be found to increase with an increase in speed limit.

Figure 4-13. Speed Limit AMF for Urban Streets.

REFERENCES


2. Harwood, D.W. NCHRP Report 282: Multilane Design Alternatives for Improving SuburbanHighways. Transportation Research Board, Washington, D.C., 1986.

3. Hadi, M.A., J. Aruldhas, L-F. Chow, and J.A. Wattleworth. “Estimating Safety Effects of Cross-Section Design for Various Highway Types Using Negative Binomial Regression.”



Transportation Research Record 1500. Transportation Research Board, Washington, D.C.,1995, pp. 169-177.

4. Hauer, E., F.M. Council, and Y. Mohammedshah. “Safety Models for Urban Four-LaneUndivided Road Segments.” Transportation Research Record 1897. Transportation ResearchBoard, Washington, D.C., 2004.

5. Bonneson, J.A., and P.T. McCoy. NCHRP Report 395: Capacity and Operational Effects ofMidblock Left-Turn Lanes. Transportation Research Board, Washington, D.C., 1997.

6. Bowman, B.L., R.L. Vecellio, and J. Miao. “Vehicle and Pedestrian Accident Models for MedianLocations.” Journal of Transportation Engineering. Vol. 121, No. 6. American Society of CivilEngineers, Washington, D.C., Nov./Dec. 1994, pp. 531-537.


8. Thakkar, J.S. “Study of the Effect of Two-Way Left-Turn Lanes on Traffic Accidents.”Transportation Research Record 960. Transportation Research Board, Washington, D.C., 1984,pp. 27-33.

9. McCoy, P.T., M. Ramanujam, M. Moussavi, and J.L. Ballard. “Safety Comparison of Types ofParking on Urban Streets in Nebraska.” Transportation Research Record 1270. TransportationResearch Board, Washington, D.C., 1990, pp. 28-41.

10. Box, P.C. “Angle Parking Issues Revisited.” ITE Journal. Institute of TransportationEngineers, Washington, D.C., March 2002, pp. 36-47.





15. Sawalha, Z., and T. Sayed. “Evaluating Safety of Urban Arterial Roadways.” Journal ofTransportation Engineering. American Society of Civil Engineers, Reston, Virginia,March/April 2001, pp. 151-158.

Chapter 5 Interchange Ramps


Chapter 5Interchange Ramps

Page


SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5Interchange Ramps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6

Bauer and Harwood Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7Khorashadi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9Comparison of Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10

Ramp Speed-Change Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16



INTRODUCTION

Access to and from grade-separated facilities is achieved using interchange ramps. Theseramps are essentially free-flow facilities with one or more lanes that allow ramp traffic to merge withfreeway traffic while maintaining a relatively high speed. Ramps can connect two freeway facilities,a freeway to an arterial, or two arterial roadways. Ramps are configured in a variety of shapes toaccommodate heavy turn movements and topography. They are associated with more significantcrash risk because of the significant speed change that occurs along their length, often coupled withhorizontal curves of near-minimum radius and relatively steep grade changes. These attributescomplicate the ramp driving task. In recognition of this complexity, driveways and intersections arerarely allowed along the length of a ramp because the associated turning traffic would unnecessarilycompound the complexity of the ramp driving task.

The development of a safe, efficient, and economical interchange ramp design typicallyreflects the consideration of a variety of design alternatives. Interchange design is particularlychallenging because of the interchange’s significant right-of-way requirement and construction cost.A variety of techniques exist for estimating the operational benefits of interchange alternatives; manyare automated through software tools. Techniques for estimating construction and right-of-way costsare also available to the designer. Unfortunately, techniques for estimating the safety benefits ofalternative designs are not as readily available. This chapter summarizes information in the literaturethat can be used to estimate the crash frequency associated with various ramp design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various interchange ramp design components and safety. Thisinformation is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in Chapter 5 of the RoadwaySafety Design Workbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical interchange ramp. They include variables for the volume of the conflictingtraffic streams. They also include variables for other factors considered to be correlated with crashfrequency (e.g., lane width, grade, etc.). One or more AMFs can be multiplied by the expected crashfrequency obtained from the prediction model to produce an estimate of the expected crash frequencyfor a specific interchange ramp.

Scope

This chapter addresses the safety of the interchange ramp and its terminal with the main lanes(i.e., the speed-change lane). For this reason, the crashes addressed herein are referred to as “ramp-related” or “speed-change-lane-related” crashes. Crashes that occur on the ramp approach to theramp-crossroad terminal are considered ramp related. However, crashes that occur within the curb-



TIGHT URBAN DIAMOND w ithFrontage Roads

REVERSE DIAMOND or X INTERCHANGE

line limits of the ramp-crossroad terminal are not considered to be ramp related. At this time, thesafety of frontage road segments is not addressed.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a widevariation in reporting threshold among cities and states. This variation complicates the extrapolationof crash trends found in one location to another location. Moreover, it can confound thedevelopment of safety prediction models using data from multiple agencies. Reporting thresholdis strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given ramp will be highif it is located in an area with a low reporting threshold. This problem is minimized when crash dataanalyses, comparisons, and models are based on data pertaining only to severe crashes.

The relationships described in this chapter address the aggregation of all vehicle-relatedcrashes on interchange ramps and speed-change lanes. Relationships that focus on vehicle-pedestrian and vehicle-bicycle crashes on ramps will be added in future updates to this chapter.

Most interchanges in use today are one of two types: diamond or partial cloverleaf (i.e.,“parclo”). Typical variations of both types are shown in Figure 5-1.

Diamond Interchanges Parclo Interchanges

Figure 5-1. Commonly Used Interchange Types.



The conventional, compressed, and tight urban diamond interchange types are commonlyused in Texas. In most instances, frontage roads are used with this interchange type and the rampsjoin with the frontage road in advance of, or just beyond, the crossroad. The more commonarrangement is to have the ramp merge with the frontage road in advance of its intersection with thecrossroad such that the combined traffic stream is served by the frontage-road intersection.

Parclo interchanges are much more common in states not having frontage roads; however,several are in service in Texas. The parclo A and parclo B types have two loop ramps that each serveone turn movement and ramps in all four quadrants. In contrast, the 2-quad parclo variations servetwo turn movements on each loop ramp and, thereby, minimize right-of-way requirements in twoquadrants. The generous allocation of ramps at the parclo A and parclo B results in a high capacityfor all interchanging movements. On the other hand, the 2-quad parclo variations tend to have fewerramps but at the cost of lower traffic carrying capacity.

Overview

This chapter documents a review of the literature related to interchange ramp safety. Thefocus is on quantitative information that relates severe crash frequency to various geometric designcomponents of the ramp. The review is not intended to be comprehensive in the context ofreferencing all relevant works that discuss ramp safety. Rather, the information presented herein isjudged to be the most current information that is relevant to ramp design in Texas. It is also judgedto be the most reliable based on a review of the statistical analysis techniques used and theexplanation of trends.

Where appropriate, the safety relationships reported in the literature are compared herein,with some interpretation offered as an explanation for any differences noted. The relationships aretypically presented as reported in the literature; however, the names or the units of some variableshave been changed to facilitate their uniform presentation in this document.

This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various ramp design components and severe crashfrequency. As noted previously, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 5 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels are described. The second part is devoted to the discussion of AMFs. However, there arecurrently no accident modification factors available for interchange ramps, primarily because of thepaucity of safety research on this topic. Hence, this latter part is relatively brief.


This part of the chapter describes safety prediction models that are applicable to interchangeramps. The first section in this part describes models related to the ramp proper. The second sectiondescribes models related to ramp speed-change lanes.



Diagonal Non-Free-Flow Loop Free-Flow Loop

Direct ConnectionaOuter Connection Semi-Direct Connectiona

Button Hook(to two-way

frontage road)

Scissors Ramp(to two-way

frontage road)

Slip Ramp(to one-way

frontage road)

a When used in directional interchanges

Interchange Ramps

Nine ramp configurations are addressed in this section. Exit ramp variations of eachconfiguration are illustrated in Figure 5-2. Entrance ramp versions have a similar alignment.

Figure 5-2. Basic Interchange Ramp Configurations. (2)

This section summarizes the findings from two recent research projects that evaluated thesafety of interchange ramp configurations. Both of these studies examined the relationship betweenvarious elements of the ramp geometry and the interchange environment. In general, they did notfind significant correlations between ramp geometry, or interchange environment, and crashfrequency. The most significant correlations were found to be with ramp configuration and rampvolume. Of particular note is the finding that ramp length is not correlated with the frequency oframp-related crash frequency.



C ' 0.0957 ftype

ADTR

1000

0.85

(5-1)

Bauer and Harwood Model

The safety prediction model developed by Bauer and Harwood (2) is based on data obtainedfrom Washington State for the years 1993 to 1995. It includes data for 533 crashes at 551interchange ramps. Their model predicts the frequency of severe ramp-related crashes. It is shownbelow as Equation 5-1.

where:C = frequency of severe ramp-related crashes, crashes/yr;

ADTR = average daily traffic on the ramp, veh/d; andftype = crash adjustment factor for area type, ramp type, and ramp configuration (see Table 5-1).

Equation 5-1 predicts only those severe crashes that occur on the ramp. The predicted crashfrequency does not include crashes associated with the ramp speed-change lanes or those that occurwithin the curb-line limits of the ramp junction at the crossroad.

The adjustment factor ftype in Equation 5-1 is used to adapt the model to alternativecombinations of area type, ramp type, and ramp configuration. The regression analysis reported byBauer and Harwood (2) indicated that the factors listed in columns 3 and 6 of Table 5-1 areappropriate for this purpose. The free-flow loop, semi-direct connection, and direct connectionramps were not found to be significantly different, so they are grouped together in the table.

Table 5-1. Crash Adjustment Factors for Equation 5-1.Area Type: Rural Area Type: Urban

RampType

RampConfiguration

ftype RampType

RampConfiguration

ftype

Exit Diagonal 1.00 Exit Diagonal 1.40Non-free-flow loop 1.97 Non-free-flow loop 2.77Free-flow loop & direct 1 0.59 Free-flow loop & direct 1 0.83Outer connection 1.30 Outer connection 1.82

Entrance Diagonal 0.58 Entrance Diagonal 0.81Non-free-flow loop 1.14 Non-free-flow loop 1.60Free-flow loop & direct 1 0.34 Free-flow loop & direct 1 0.48Outer connection 0.75 Outer connection 1.05

Note:1 - Category includes free-flow loop, semi-direct connection, and direct connection ramps.



0.0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000 2500 3000

Average Daily Traffic Demand, veh/d

Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Non-Free-Flow Loop

Outer Connection

Free-Flow Loop & Direct

Diagonal

Rural Exit Ramp

0.0

0.1

0.2

0.3

0.4

0.5

0 500 1000 1500 2000 2500 3000


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Non-Free-Flow Loop

Outer Connection

Free-Flow Loop & DirectDiagonal

Rural Entrance Ramp

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3000 5000 7000 9000 11000 13000 15000


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Non-Free-Flow Loop

Outer Connection

Free-Flow Loop & Direct

Diagonal

Urban Exit Ramp

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3000 5000 7000 9000 11000 13000 15000


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Non-Free-Flow Loop

Outer Connection

Free-Flow Loop & DirectDiagonal

Urban Entrance Ramp

The adjustment factors ftype in Table 5-1 vary from 0.34 to 2.77, depending on thecombination of attributes associated with a specific ramp. This range is relatively wide and suggeststhat ramp type and configuration can have a significant impact on safety.

The relationship between severe crash frequency and ramp configuration is shown inFigure 5-3. The trends shown are based on Equation 5-1 and the factors in Table 5-1. The rampvolume range used in the figures reflects typical volume levels in urban and rural environments andare consistent with the volume levels reported by Bauer and Harwood.

a. Rural Exit Ramps. b. Rural Entrance Ramps.

c. Urban Exit Ramps. d. Urban Entrance Ramps.

Figure 5-3. Severe Crash Frequency Predicted by Bauer and Harwood Model.

The trends in Figure 5-3 indicate that non-free-flow loop ramps experience the most crashes.Outer connection ramps experience fewer crashes, followed by diagonal ramps and free-flow-loopramps. A comparison across ramp types indicate that exit ramps are associated with between 35 and65 percent more crashes than entrance ramps.



Khorashadi Model

Khorashadi (3) examined severe crash frequency at 13,325 interchanges in California. Heassembled a database that included information about ramp configuration, ramp volume, and crashfrequency. The database represented the crash history for three years and included 24,143 severecrashes. Khorashadi did not develop a regression model similar to Equation 5-1. Rather, hecomputed the severe crash rate for each ramp configuration. These rates are summarized inTable 5-2; they were obtained from Appendix B of the report by Khorashadi. In general, crash datafor 240 interchange ramps underlie each of the crash rates reported in Table 5-2; however, for anysingle rate, the number ranges from 1 to 2000 ramps.

Table 5-2. Severe Crash Rates Reported by Khorashadi (3).Area Type: Rural Area Type: Urban

Ramp Type RampConfiguration

Crash Rate 1

crashes/mvRamp Type Ramp

ConfigurationCrash Rate 1

crashes/mvExit Diagonal 0.183 Exit Diagonal 0.467

Non-free-flow loop 0.887 Non-free-flow loop 0.387Free-flow loop 0.239 Free-flow loop 0.318Semi-direct connection 0.691 Semi-direct connection 0.188Direct connection 0.235 Direct connection 0.307Button hook 1.670 Button hook 0.568Scissor 0.553 Scissor 0.468Slip not available Slip 0.356

Entrance Diagonal 0.186 Entrance Diagonal 0.186Non-free-flow loop 0.228 Non-free-flow loop 0.317Free-flow loop 0.150 Free-flow loop 0.196Semi-direct connection 0.488 Semi-direct connection 0.192Direct connection 0.141 Direct connection 0.268Button hook 0.254 Button hook 0.229Scissor 0.077 Scissor 0.212Slip not available Slip 0.225

Note:1 - Crash rate is in units of severe crashes per million ramp vehicles.

Examination of the rates in Table 5-2 indicates that the button hook ramp experiences themost crashes. This configuration is closely followed by the non-free-flow loop ramp. Thereafter,in order of decreasing crash rate, are the scissor ramp and the slip ramp. The diagonal, semi-directconnection, and direct connection ramps tend to experience about the same low crash rate. Acomparison across ramp types indicates that exit ramps are associated with between 55 and65 percent more crashes than entrance ramps. There is no apparent pattern between the crash ratesin urban and rural environments.



C ' 0.000365 CR ADTR (5-2)

ln(CR) ' b0 % b1 Idiag % b2 Inff % b3 Iff % b4 Ioc % b5 Isd % b6 Iexit (5-3)

The severe crash frequency for a specific ramp can be estimated using Equation 5-2 and therates in Table 5-2.

where:C = frequency of severe ramp-related crashes, crashes/yr; and

CR = severe crash rate (see Table 5-2), crashes/million ramp vehicles.


The crash models described in the previous subsections are examined in this subsection todetermine if there is general agreement about the relative safety of common ramp configurations.To facilitate this analysis, Equation 5-1 was used to compute severe crash frequencies for a rangeof volumes typically found in urban and rural environments. These frequencies, shown in Figure 5-3, were used to compute an equivalent crash rate for each area type, ramp type, and rampconfiguration. These rates were then compared to those in Table 5-2 for common rampconfigurations.

A regression model was used to facilitate the comparison of crash rates. The model usesindicator variables for the various ramp configurations as well as for the two ramp types (i.e.,exit/entrance) and the two area types (i.e., urban/rural). The following model form was used:

where:ln(CR) = natural log of severe crash rate;

Idiag = indicator variable for diagonal ramp (1 if diagonal ramp; 0 otherwise);Inff = indicator variable for non-free-flow ramp (1 if non-free-flow ramp; 0 otherwise);Iff = indicator variable for free-flow ramp (1 if free-flow ramp; 0 otherwise);Isd = indicator variable for semi-direct connection (1 if semi-direct connection; 0 otherwise);Ioc = indicator variable for outer connection (1 if outer connection; 0 otherwise); and

Iexit = indicator variable for exit ramp (1 if exit ramp; 0 if entrance ramp).

An indicator variable for area type was originally included in Equation 5-3 but was not foundto be statistically significant, so it was removed from the model. Indicator variables for the buttonhook, scissor, and slip ramps were also originally included in Equation 5-3 but the predicted rateswere not intuitive, so they were separately evaluated. This evaluation is described later in thissubsection.

The natural log function is used in Equation 5-3 because it bounds the predicted rates to non-negative values, as is appropriate for the analysis of crash data. The predictive capability of themodel is shown in Figure 5-4. The coefficient of determination R2 of the regression model is 0.55.



0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Predicted Severe Crash Rate, crashes/mv

Rep

orte

d Se

vere

Cra

sh R

ate,

cr

ashe

s/m

v 11

Figure 5-4. Comparison of Predicted and Reported Crash Rates.

As the trends in the data in Figure 5-4 suggest, there is reasonably good agreement betweenthe predicted crash rates and those obtained from the models developed by the two researchers.Three of the crash rates from the Khorashadi database were found to be much higher than predictedby the regression model. These three rates apply to the exit non-free-flow loop, exit semi-directconnection, and the entrance semi-direct connection ramps; all of which are located in a ruralenvironment. These rates were obtained from a total of 85 ramps, which is a relatively small numbercompared to the other configurations. In fact, the highest rate of 0.887 is based on crashes on onlyfour non-free-flow loop ramps. Hence, these rates likely reflect the occurrence of an atypically largenumber of crashes on the corresponding ramps in the three-year period. Crash frequency likelyreturned to values nearer that predicted by the regression model in subsequent years.

The severe crash rates predicted by the calibrated form of Equation 5-3 are listed inTable 5-3. In application, these rates would be used with Equation 5-2 to estimate the severe crashfrequency associated with a specific ramp type, ramp configuration, and ramp volume. These ratesrelate to only those severe crashes that occur on the ramp. The predicted crash frequency does notinclude crashes associated with the ramp speed-change lanes or those that occur within the curb-linelimits of the ramp junction at the crossroad.

These rates listed in Table 5-3 confirm the trends noted in the evaluation of the previous twomodels. Specifically, that crash rates for entrance ramps are about 60 percent of those for exit ramps.The button hook ramp is associated with the largest crash rate, followed closely by that for the non-free-flow loop. The scissor and slip ramps have the next highest rates followed by the outerconnection ramp and the diagonal ramp. The semi-direct connection ramp, the direct connection,and the free-flow loop ramp have the lowest crash rates. It should be noted that crash ratesassociated with frontage-road ramps have crash rates that are 30 to 100 percent larger than those forthe diagonal ramp, a ramp that is common to diamond interchanges in non-frontage-road settings.



CR '

CRrural

s 2rural

%CRurban

s 2urban

1

s 2rural

%1

s 2urban

(5-4)

Table 5-3. Severe Crash Rates for Various Ramp Configurations.Ramp Type Ramp


crashes/mvRamp Type Ramp


crashes/mvExit Diagonal 0.277 Entrance Diagonal 0.168

Non-free-flow loop 0.507 Non-free-flow loop 0.308Free-flow loop 0.205 Free-flow loop 0.124Outer connection 0.332 Outer connection 0.201Semi-direct connection 0.252 Semi-direct connection 0.153Direct connection 0.209 Direct connection 0.127Button hook 0.573 Button hook 0.275Scissor 0.484 Scissor 0.208Slip 0.356 Slip 0.225


The crash rates for the button hook, scissor, and slip ramps were not part of the regressionanalysis using Equation 5-3. These ramps did not follow the trends apparent in the rates for the otherramps so they were evaluated separately. The estimate of the button hook and the scissor ramp crashrates was based on the following equation:

where:s = standard deviation of the average crash rate, crashes/yr.

Equation 5-4 provides a weighted average of the crash rates for the rural and urban areatypes, for a common ramp type and ramp configuration. The weighting factor is that of the inverseof the variance of the average rate. Thus, the rates with a large amount of uncertainty are given lessweight in the computed average rate. The original rates and their corresponding standard deviationsare shown in Table 5-4. These standard deviations were obtained from Appendix B of the report byKhorashadi (3).

The rates for rural and urban interchanges were combined based on the aforementionedregression analysis wherein it was found that there was no significant difference between the crashrates in rural and in urban areas. Equation 5-4 was applied to the button hook and the scissor rampsbecause each ramp configuration was found in urban and rural locations. The weighted average ratesare listed in Table 5-3. Equation 5-4 could not be applied to the slip ramps because they were onlyfound in urban areas. Hence, the original rates for slip ramps are repeated in Table 5-3.



Table 5-4. Severe Crash Rate Analysis for Frontage-Road Ramps.Area Type: Rural Area Type: Urban

RampType

RampConfiguration

Crash Rate 1

crashes/mvStandardDeviation

crashes/mv

RampType

RampConfiguration

Crash Rate 1

crashes/mvStandardDeviation

crashes/mvExit Button hook 1.670 0.774 Exit Button hook 0.568 0.055

Scissor 0.553 0.143 Scissor 0.468 0.069Slip not available -- Slip 0.356 0.191

Entrance Button hook 0.254 0.098 Entrance Button hook 0.229 0.024Scissor 0.077 0.061 Scissor 0.212 0.035Slip not available -- Slip 0.225 0.140


Ramp Speed-Change Lanes

A model for estimating the severe crash frequency associated with the ramp speed-changelane is the subject of this section. The crash rates provided in Table 5-3 do not include crashes thatoccur in speed-change lanes. Speed-change lanes are the location of a majority of conflicts betweenramp traffic and mainlane traffic. Thus, the design of the speed-change lane is likely to have asignificant influence on ramp safety. Speed-change lanes associated with an interchange ramp arethe subject of this section. These lanes function as either an acceleration lane or a deceleration lane.Both types of speed-change lane are shown in Figure 5-5.

Bauer and Harwood (2) developed several models relating crash frequency to the designelements of ramp speed-change lanes. Separate models were developed for predicting total (i.e.,property-damage-only plus severe crashes) crashes for acceleration lanes, total crashes fordeceleration lanes, and severe crashes for acceleration lanes on diagonal ramps. There wasinsufficient data in their database to develop severe crash models for deceleration lanes or for otherramp configurations. As a result, the models described in this section are those developed by Bauerand Harwood (2) for predicting total crashes. However, an adjustment factor has been added to eachmodel such that it estimates severe crash frequency.



Caccel ' 0.00702ADTR

1000

0.98 ADTM

1000

0.32

e (6.88La & 0.59 Irural) (1 & 0.01 PDOa ) (5-5)

Cdecel ' 0.0261ADTR

1000

1.04

e (0.09 Ws & 1.21 Irural) (1 & 0.01 PDOd ) (5-6)

Figure 5-5. Acceleration and Deceleration Speed-Change Lanes. (2)

Bauer and Harwood’s model for total crashes in an acceleration lane is:

where:Caccel = frequency of severe crashes on acceleration lanes, crashes/yr;

ADTM = average daily traffic in adjacent freeway lanes (one-way), veh/dLa = length of acceleration lane, mi;

Irural = indicator for area type (1 if rural, 0 if urban); andPDOa = percent property-damage-only crashes in acceleration lanes (= 52.2).

Bauer and Harwood’s model for all crashes in a deceleration lane is:



0.0

0.1

0.2

0.3

0.4

0.5

0 2000 4000 6000 8000

Average Daily Ramp Traffic Demand, veh/d

Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Mainlane ADT = 10 x Ramp ADT

Acceleration Lane Urban Rural

Deceleration Lane Urban Rural

where:Cdecel = frequency of severe crashes on deceleration lanes, crashes/yr;

PDOd = percent property-damage-only crashes in deceleration lanes (= 52.6); andWs = right shoulder width, ft.

Equations 5-5 and 5-6 were derived to predict total crashes, as opposed to severe crashes.An adjustment multiplier of “1 !0.01 PDO” was added to each equation to convert the predictioninto severe crash frequency. This term requires an estimate of the percentage of PDO crashes. Thispercentage is estimated at 52.2 and 52.6 percent for acceleration lanes and deceleration lanes,respectively, based on the database description provided by Bauer and Harwood (2).

The factor for acceleration length in Equation 5-5 and for shoulder width in Equation 5-6 arecounter-intuitive in terms of their influence on the corresponding model prediction. The positivesign associated with the acceleration length coefficient implies that longer acceleration lane lengthsare associated with more crashes. Logically, a longer acceleration length would be associated witha lower speed differential between mainlane and merging ramp vehicles, which would suggest a saferoperation. Similarly, the positive sign of the shoulder width coefficient implies an increase incrashes with wider shoulders. Accident modification factors developed for highways and streetshave consistently shown that crashes are reduced with an increase in shoulder width. As a result,accident modification factors for acceleration lane length and ramp shoulder width cannot be derivedfrom these model terms.

Figure 5-6 illustrates the safety prediction models for ramp speed-change lanes. It is basedon an average acceleration lane length of 0.23 mi (1200 ft) and a right shoulder width of 8 ft. Thesedimensions represent average values found in the database used by Bauer and Harwood (2).

Figure 5-6. Crash Frequencies for Ramp Speed-Change Lanes.



The trends in Figure 5-6 indicate that acceleration lanes have about twice the severe crashfrequency as deceleration lanes. They also indicate that speed-change lanes in urban areas haveabout twice the number of crashes as found at speed-change lanes in rural areas.


At this time, there are no AMFs available from the literature that relate crash frequency tointerchange ramp geometry, access control, or related factors. It could be rationalized that the AMFsdescribed in other chapters (e.g., those for lane width, shoulder width, grade, etc.) would also beapplicable to ramps. However, interchange ramps have unique operational characteristics (e.g., one-way operation, significant speed change along the ramp) that would likely preclude the use of AMFsdeveloped for highway segments.

REFERENCES


2. Bauer K.M., and D.W. Harwood. Statistical Models of Accidents on Interchange Ramps andSpeed-Change Lanes. Report No. FHWA-RD-97-106. Federal Highway Administration,Washington, D.C., 1997.

3. Khorashadi, A. Effect of Ramp Type and Geometry on Accidents. FHWA/CA/TE-98/13.California Department of Transportation, Sacramento, California, November 1998.

Chapter 6 Rural Intersections


Chapter 6Rural Intersections

Page


SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5Rural Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5

Vogt Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5Harwood Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6Comparison of Signalized Intersection Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7

Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8Bauer and Harwood Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8Vogt Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-10Comparison of Unsignalized Intersection Crash Models . . . . . . . . . . . . . . . . . . . . . . 6-11

Development of Representative Intersection Crash Rates . . . . . . . . . . . . . . . . . . . . . . . . . 6-12

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15Rural Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15

Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15Left-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-16Right-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-17Number of Lanes on the Major and Minor Roads . . . . . . . . . . . . . . . . . . . . . . . . . 6-17Alignment Skew Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19Intersection Sight Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19

Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-21

Truck Presence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-21Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-22

Rural Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24

Left-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25Right-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25Number of Lanes on the Major and Minor Roads . . . . . . . . . . . . . . . . . . . . . . . . . 6-26Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26Median Presence and Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26Alignment Skew Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-29Intersection Sight Distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-30

Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-31Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-32

Truck Presence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-32Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-33

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-34



INTRODUCTION

At intersections, drivers face a multitude of choices related to path, speed, and route that, incombination with numerous conflicting movements, complicate the driving task and significantlyincrease the potential for a crash. In Texas, about one-third of all crashes on rural highways occurat intersections. These crashes are consistently more severe than those experienced at urbanintersections--primarily because of the high-speed nature of the rural highway. Safety improvementsat rural intersections are often focused on design elements that provide separation for turningmovements, increased driver visibility and sight lines, and traffic control devices that heighten driverawareness of the intersection’s presence.

The development of a safe, efficient, and economical rural intersection design may reflectconsideration of a wide variety of design alternatives. A variety of techniques exist for estimatingthe operational benefits of alternatives; many are automated through software tools. Techniques forestimating construction and right-of-way costs are also available to the designer. Unfortunately,techniques for estimating the safety benefits of alternative designs are not as readily available. Thischapter summarizes information in the literature that can be used to estimate the crash frequencyassociated with various rural intersection design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various rural intersection design components and safety. Thisinformation is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in Chapter 6 of the RoadwaySafety Design Workbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical rural intersection. They include variables for the volume of the conflictingtraffic streams. They also include variables for other factors considered to be correlated with crashfrequency (e.g., median type, functional class, etc.). One or more AMFs can be multiplied by theexpected crash frequency obtained from the prediction model to produce an estimate of the expectedcrash frequency for a specific intersection.

Scope

This chapter addresses the safety of intersections in a rural area. As such, the crash typesused to describe the level of safety are identified as “intersection related.” The intersectionrelationship of a crash is indicated on the crash report or, in some instances, is determined by theresearchers. If the researchers determine the intersection-relationship of a crash, it is oftentimesbased on crash location relative to the intersection (2). Specifically, all crashes that occur within aspecified distance back from the intersection are labeled as “intersection related.” The combinationof crash location and type (e.g., turn related or multi-vehicle) has also been used by some researchers



to identify intersection relationship. Crashes that are not intersection related are referred to hereinas “mid-block” crashes and are the subject of Chapter 3.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a widevariation in reporting threshold among counties and states. This variation complicates theextrapolation of crash trends found in one location to another location. Moreover, it can confoundthe development of safety prediction models using data from multiple agencies. Reporting thresholdis strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given road will be highif it is located in a state with a low reporting threshold. This problem is minimized when crash dataanalyses, comparisons, and models are based on data pertaining only to severe crashes.

Overview

This chapter documents a review of the literature related to rural intersection safety. Thefocus is on quantitative information that relates severe crash frequency to various geometric designcomponents of the rural intersection. The review is not intended to be comprehensive in the contextof referencing all relevant works that discuss rural intersection safety. Rather, the informationpresented herein is judged to be the most current information that is relevant to rural highway designin Texas. It is also judged to be the most reliable based on a review of the statistical analysistechniques used and the explanation of trends.


This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various intersection design components and severe crashfrequency. As noted previously, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 6 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels reported in the literature are described. In the second part, accident modification factors aredescribed for various geometric design and traffic control components. In each of these parts, thereis a separate discussion of signalized and unsignalized intersections.



C ' 0.03854 Q 0.2358major Q 0.2358

minor e B1 (6-1)

B1 ' &0.2943 Imp & 0.0113 Plt % 0.0822 Gr % 0.0323 Pt (6-2)

Gr ' 100 j|g2 & g1 |

Lvc(6-3)


Described in this part of the chapter are several safety prediction models that were developedto estimate the expected frequency of intersection-related crashes. The discussion is separated intotwo sections with one section describing models that apply to signalized intersections and a secondsection describing models that apply to unsignalized intersections. At the end of each section, themodels are compared in terms of the relationship between severe crash frequency and traffic volume.

All of the models presented in this part of the chapter make reference to the “major” and“minor” roadways that form the intersection. These models are based on the assumption that the“major road” is the road with the higher volume of the two roads. It most instances, this assumptionis in agreement with the number of lanes provided and the functional class of the two roads.However, in some instances, this assumption may mean that a road with more lanes or a higherfunctional classification but with lower volume will need to be specified as the “minor” road for thepurpose of using a safety prediction model.

Rural Signalized Intersections

This section addresses safety prediction models for rural signalized intersections. Two setsof models are described and are identified by the names of their developers. They include:

! Vogt Model! Harwood Model

Vogt Model

Vogt (2) investigated the relationships between crash frequency and various rural intersectiongeometry and operational attributes. He developed a series of safety prediction models for a varietyof intersection configurations and control conditions. The model he developed for four-leg ruralsignalized intersections is described in this subsection. The models he developed for three-leg andfour-leg rural unsignalized intersections are discussed in a later section.

Vogt’s model for predicting severe crash frequency at four-leg rural signalized intersectionsis:

with,

and

where:



C = frequency of severe intersection-related crashes, crashes/yr;Qmajor = total daily volume on major-road (both directions), veh/d;Qminor = total daily volume on minor-road (both directions), veh/d;

Imp = signal phasing indicator variable (1 if more than 2 phases; 0 otherwise);Plt = minor-road left-turn percentage during the peak hour, %;Gr = average grade rate for all vertical curves within 800 ft of the intersection, %/ft;gi = grade of vertical curve tangent i (i = 1 for entry tangent and 2 for exit tangent), %;

Lvc = length of vertical curve, ft; andPt = percent trucks during the peak hour (average for all intersection movements), %.

It should be noted that the model predicts fewer crashes when the minor road has more leftturns. This trend is illogical and is likely correlated with other factors that are present at intersectionswith numerous left turns. No justification or rationale was offered by the researchers for thiscounter-intuitive trend.

The characteristics of the data used by Vogt (2) are summarized in Table 6-1. As this tableindicates, their models are based on three years of crash data for each of 49 rural intersections. Assuggested by a comparison of the two databases described, the database used by Vogt is the sameas that used by Harwood et al. (3) (and described in the next subsection). However, the differencebetween the two models lies in the method used to define an intersection-related crash. Vogt definedintersection-related crashes to be all crashes that occurred at, or within 250 ft of, the intersection.Harwood et al. used a more stringent criterion in that the crashes had to occur within 250 ft and beof a type that is generally related to intersection operations.

Table 6-1. Database Characteristics for Signalized Intersection Safety Prediction Models.Model


Data Source Years of Crash data

IntersectionRelationship 1

IntersectionLegs

Number ofIntersections

Vogt (2) California DOT& Michigan DOT

3 250 ft 4 49

Harwood etal. (3)

California DOT& Michigan DOT

3 250 ft and turn-related,sideswipe, rear end, or

angle crashes.

4 49

Note:1 - Intersection relationship indicates the definition used to identify crash relationship to the intersection. Distances

listed denote the distance back from the intersection within which a crash is denoted as “intersection related.”

Harwood Model

Harwood et al. (3) investigated the relationships between crash frequency and various ruralintersection geometry and operational attributes. They developed safety prediction models for four-leg rural signalized intersections using the same database as used by Vogt (2). However, they useda different definition for identifying “intersection-related” crashes; they also considered differentfactors in their model. Their model was developed using total crash frequency (i.e., property-



C ' 0.00425 Q 0.60major Q 0.20

minor e B1 (1.0 & 0.01 PDO) (6-4)

B1 ' &0.40 Imp & 0.018 Plt % 0.11 Gr % 0.026 Pt % 0.041 dn (6-5)

damage-only, injury, and fatal crashes); however, they provided an adjustment factor that can be usedto use their model to estimate severe crash frequency.

The model developed by Harwood et al. for predicting severe crash frequency at four-legrural signalized intersections is:

with,

where:C = frequency of severe intersection-related crashes, crashes/yr; anddn = number of driveways on the major road within 250 ft of the intersection; and

PDO = property-damage-only crashes as a percentage of total crashes (= 62.3 percent), %.

It should be noted that the model predicts fewer crashes when the minor road has more leftturns. This trend is illogical and is likely correlated with other factors that are present at intersectionswith numerous left turns. No justification or rationale was offered by the researchers for thiscounter-intuitive trend. The characteristics of the data used by Harwood et al. (3) are summarizedin Table 6-1.

Comparison of Signalized Intersection Crash Models

The two models described in the previous subsections are compared in this subsection. Theobjective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. For both models, the values of the other model variables were setat typical values for rural signalized intersections. These values are listed in Table 6-2.

Table 6-2. Typical Values Used for Rural Signalized Intersection Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

Vogt (2) Harwood et al. (3)Signal phasing more than 2 phases U U

Grade rate, %/ft 0.0 (i.e., flat) U U

Percentage left turns on minor road 27 U U

Number of driveways on major road 3 -- U

Percentage of trucks, % 9 U U



C ' 0.0000113 Q 0.680major Q 0.546

minor e B1 % B2 (6-6)

0

1

2

3

4

0 5 10 15 20 25

Major-Road Volume (1000's), veh/d

Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Four-Leg IntersectionsMinor Volume = 0.2 Major Volume

Vogt (2) Harwood et al. (3)

No left-turn phase28 percent left turnsNo vertical curves9 percent trucks3 driveways on major road

Figure 6-1 illustrates the crash frequency predictions obtained from the two models. Thetrends shown indicate a general agreement that the annual severe crash frequency tends to equalbetween 3.0 and 3.5 crashes/yr when the major-road volume is 25,000 veh/d.

Figure 6-1. Comparison of Safety Prediction Models for Rural Signalized Intersections.

Rural Unsignalized Intersections

This section addresses safety prediction models for rural unsignalized intersections.Specifically, these are two-way stop-controlled (TWSC) intersections. Two sets of models aredescribed and are identified by the names of their developers. They include:

! Bauer and Harwood Models! Vogt Models

Bauer and Harwood Models

Bauer and Harwood (4) investigated the relationships between crash frequency and variousintersection geometry and operational attributes. They developed a series of safety prediction modelsfor a variety of intersection configurations and control conditions. The models they developed forthree-leg and four-leg rural TWSC intersections are discussed in this subsection. The urbanintersection models are described in Chapter 7.

Bauer and Harwood’s model for predicting severe crash frequency at rural four-leg TWSCintersections is:



with,

and

where:C = frequency of severe intersection-related crashes, crashes/yr;

Imaj3 = major-road through lanes (1 if 3 or fewer lanes; 0 otherwise);Vd = major-road design speed, mph;Iflat = terrain indicator variable (1 if flat; 0 if rolling);Imnt = terrain indicator variable (1 if mountainous; 0 if rolling);Ima = major-road functional class indicator variable (1 if minor arterial; 0 if principal arterial);Icl = major-road functional class indicator variable (1 if collector; 0 if principal arterial); and

Inolite = intersection lighting indicator variable (1 if no lighting; 0 otherwise).

It should be noted that the model predicts more crashes when the terrain is flat than when itis rolling and more when it is rolling than mountainous. The researchers note this anomaly andsuggest that this trend is likely due to a correlation between this variable and other factors.

Bauer and Harwood’s model for predicting severe crash frequency at rural three-leg TWSCintersections is:

with,

and


Inoltln = major-road left-turn channelization indicator variable (1 if no left-turn lane; 0 if paintedleft-turn lane);

Icbltln = major-road left-turn channelization indicator variable (1 if curbed left-turn lane; 0 ifpainted left-turn lane);

Ws = major-road outside shoulder width, ft; andIfrt = minor-road channelization (1 if no free right-turn lane; 0 if free right-turn lane).

B1 ' 0.385 Imaj3 % 0.013 Vd % 0.183 Iflat (6-7)

B2 ' &0.234 Imnt % 0.261 Ima % 0.170 Icl % 0.219 Inolite (6-8)

C ' 0.0000357 Q 0.781major Q 0.384

minor e B1 % B2 (6-9)

B1 ' &0.030 Ws % 0.169 Inolite % 0.180 Inoltln % 0.062 Icbltln (6-10)

B2 ' &0.219 Ifrt % 0.164 Ima % 0.192 Icl (6-11)



The regression coefficient in Equation 6-11 for right-turn channelization on the minor roadindicates that the addition of a free right-turn lane will increase crashes. This trend is likelyattributable to the yield or stop control associated with such lanes and the fact that the driver stoppedin the free right-turn lane is typically in a poor position to evaluate safe gaps in the crossing trafficstream. This poor position stems from the large-radius travel path associated with the free right-turnlane. The stop (or yield) line on this path is typically placed near the point of entry to the major roadand requires drivers to look back, over their left shoulder, to search for gaps in the conflicting trafficstream. This maneuver is difficult for most drivers and may compromise the diligence with whichthey search for safe gaps.

Although not apparent by inspection of the coefficients listed in Equations 6-6 through 6-11,an examination of model predictions indicates that three-leg intersections have between 50 and60 percent of the crashes experienced by four-leg intersections, for similar volume levels.

The characteristics of the data used by Bauer and Harwood (4) are summarized in Table 6-3.They used three years of crash data for each of 4126 rural intersections. They defined intersection-related crashes to be all crashes that occurred at, or within 250 ft of, the intersection.

Table 6-3. Database Characteristics for Unsignalized Intersection Safety Prediction Models.Model




IntersectionLegs


Bauer &Harwood (4)

California DOT 3 250 ft 3 26924 1434

Vogt (2) California DOT& Michigan DOT

3 250 ft 3 844 72



Vogt Models

Vogt (2) developed a series of safety prediction models for rural TWSC intersections. Onemodel was calibrated for four-leg intersections and a second was calibrated for three-legintersections. The model for predicting severe crash frequency at rural four-leg intersections is:

His model for predicting severe crash frequency at rural three-leg intersections is:

C ' 0.0000530 Q 0.7224major Q 0.4778

minor (6-12)

C ' 0.0000019 Q 1.2028major Q 0.1925

minor (6-13)



Although not apparent by inspection of the coefficients listed in Equations 6-12 and 6-13,an examination of model predictions indicates that three-leg intersections have between 35 and45 percent of the crashes experienced by four-leg intersections, for similar volume levels.

The characteristics of the data used by Vogt (2) are summarized in Table 6-3. He used threeyears of crash data for each of 156 rural intersections. He defined all crashes occurring at, or within250 ft of, the intersection as “intersection related.”

Comparison of Unsignalized Intersection Crash Models

The models described in the previous subsections are compared in this subsection. Theobjective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. The models were grouped into three-leg and four-leg categories.For the Bauer and Harwood (4) model, the values of the model variables were set at typical valuesfor rural unsignalized intersections. These values are listed in Table 6-4.

Table 6-4. Typical Values Used for Rural Unsignalized Intersection Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

Vogt (2) Bauer & Harwood (4)

Shoulder width, ft 6.0 -- U

Terrain flat -- U

Number of lanes on major road 2 -- U

Free right-turn lanes on minor road no -- U

Left-turn channelization on major road no -- U

Free right-turn lanes on minor road no -- U

Functional class of major road principal arterial -- U

Design speed of major road, mph 55 -- U

Intersection lighting no -- U

Typical values listed in Table 6-4 are based on the median values for each variable in thedatabase used by Bauer and Harwood (4, Tables 2 and 6).

Figure 6-2 illustrates the crash frequency predictions obtained from the various models. Thetrends shown indicate a general agreement that the annual severe crash frequency for four-legintersections tends to equal about 2.7 crashes/yr when the major-road volume is 20,000 veh/d. Thethree-leg intersection trends are also in general agreement. The trends shown suggest that the annualsevere crash frequency for three-leg intersections tends to equal about 1.1 crashes/yr when the major-road volume is 20,000 veh/d.



CR '106

365α Q

β1major Q

β2minor

Qmajor % Qminor

(6-14)

α ' αb % e (other terms ) (6-15)

CR ' 2740α Q

β1 % β2 & 1major r β2

1 % r(6-16)

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr

Three-Leg IntersectionsMinor Volume = 0.05 Major Volume

Bauer & Harwood (3)No free right-turn lanesNo left-turn channelizationNo lightingMajor arterial6 ft shoulder width

Vogt (2)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 5 10 15 20


Seve

re C

rash

Fre

quen

cy,

cras

hes/

yr


Vogt (2)

Bauer & Harwood (3)Flat terrainTwo lanes on major roadNo lightingPrincipal arterial55 mph design speed

a. Four-Leg Intersections. b. Three-Leg Intersections.

Figure 6-2. Comparison of Safety Prediction Models for Rural Unsignalized Intersections.

Development of Representative Intersection Crash Rates

The safety prediction models previously presented are examined more closely in this sectionfor the purpose of developing representative intersection crash rates. A generalized equation wasdeveloped for estimating the average crash rate. The equation is:

with,

where:CR = severe crash rate for intersection-related crashes, crashes/million-vehicle-miles (mvm);α = regression constant that combines αb with all exponential terms at their average value; andαb = regression constant obtained from multivariate regression model.

The numerator of this equation includes the basic structure of the safety prediction modelsdescribed previously. The constant of “106/365” in Equation 6-14 is included to convert the rateinto traditional crash rate units–crashes per million entering vehicles. Equation 6-14 was simplifiedto the following form by substituting the ratio of the minor-road to major-road entering flows r:

where:r = ratio of minor-road to major-road daily volumes (= Qminor / Qmajor).



α ' e &16.52 % 1.60 Nleg (6-17)

β1 % β2 & 1 ' &0.768 & 0.096 ln(α) (6-18)

R2 = 0.62

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-14.0 -12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0

alpha

b2

Rural outliersRuralUrban

R2 = 0.93

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-14.0 -12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0

alpha

b1 +

b2 -

1As a next step in the examination, the relationship between α, β1, β2, and various variables

describing intersection control and number of approach legs was investigated. The values of α, β1,β2 were obtained from the models previously described. To supplement this database, someadditional values of α, β1, β2 were obtained from some models developed by Vogt and Bared (5,Tables 36 and 37) for predicting severe crash frequency. For this analysis, a variable alpha wascomputed as the natural log of α (i.e., alpha = ln[α]). Figure 6-3a illustrates the relationship foundbetween alpha and the sum “β1 + β2 !1” (where β1 and β2 are labeled b1 and b2, respectively).

a. Correlation between Alpha and “β1 + β2 !1.” b. Correlation between Alpha and β2.

Figure 6-3. Correlation between Model Coefficients.

Figure 6-3b illustrates the relationship found between α and β2. The circular data points inthis figure represent the database of α and β2 values applicable to rural intersections. Two of the datapoints (shown as open circles) did not follow the pattern in the remaining database and wereexcluded from further analysis. The remaining database included only one pair of values forsignalized intersections; all others were for unsignalized intersections. As a result, the ruralintersection database was not adequate for evaluating the effect of intersection control mode on β2.To overcome this limitation, the database was expanded to include α and β2 values for urbansignalized and unsignalized intersections (see Chapter 7). These values are shown in Figure 6-3busing a “+” symbol. In general, the trends in Figures 6-3a and 6-3b illustrate that the variables alpha,β1, and β2 are correlated with each other. Although not shown, they were also found to be correlatedwith control mode. A subsequent analysis indicated a similar correlation between alpha and thenumber of intersection legs (R2 = 0.31).

The following relationships were derived based on the analysis of model coefficients:

with,



β2 ' &0.638 % 0.122 Nleg % 0.080 Isig & 0.066 ln(α) (6-19)

C ' CR 365106

(Qmajor % Qminor ) (6-20)

and

where:Nleg = number of intersection legs (3 or 4); andIsig = indicator variable for intersection control mode (1 for signalized; 0 otherwise).

Equations 6-17, 6-18, and 6-19 were used with Equation 6-16 to compute equivalent crashrates for various combinations of intersection control and number of approach legs. The findingsfrom this analysis are presented in Tables 6-5 and 6-6 for three-leg and four-leg rural intersections,respectively.

Table 6-5. Severe Crash Rates for Three-Leg Rural Intersections.ControlMode

Major-RoadVolume, veh/d

Crash Rate, severe crashes per million-vehicle-milesRatio of Minor-Road to Major-Road Volume

0.05 0.10 0.15 0.20 0.25Unsignalized 5000 0.10 0.14 0.16 0.18 0.19

10,000 0.13 0.18 0.21 0.23 0.2515,000 0.15 0.20 0.24 0.26 0.2820,000 0.17 0.23 Intersection very likely to meet signal

warrants25,000 0.18Signalized 5000 0.08 0.11 0.14 0.16 0.17

10,000 0.10 0.15 0.18 0.20 0.2215,000 0.12 0.17 0.21 0.23 0.2520,000 0.13 0.19 0.23 0.26 0.2825,000 0.14 0.20 0.25 0.28 0.3030,000 0.15 0.22 0.26 0.30 0.3340,000 0.17 0.24 0.29 0.33 0.36$50,000 0.18 0.26 0.32 0.36 0.39

The following equation should be used to estimate severe crash frequency in conjunctionwith the crash rates listed in Tables 6-5 or 6-6:



Table 6-6. Severe Crash Rates for Four-Leg Rural Intersections.ControlMode

Major-RoadVolume, veh/d

Crash Rate, severe crashes per million-vehicle-milesRatio of Minor-Road to Major-Road Volume

0.10 0.30 0.50 0.70 0.90Unsignalized 5000 0.18 0.26 0.30 0.31 0.32

10,000 0.20 0.30 0.34 0.36 0.3615,000 0.22 0.33 0.37 0.39 0.4020,000 0.23 Intersection very likely to meet signal warrants25,000 0.25

Signalized 5000 0.15 0.24 0.28 0.30 0.3110,000 0.17 0.28 0.32 0.35 0.3615,000 0.18 0.30 0.35 0.38 0.3920,000 0.20 0.32 0.37 0.40 0.4225,000 0.20 0.33 0.39 0.42 0.4430,000 0.21 0.35 0.41 0.44 0.4540,000 0.23 0.37 0.43 0.46 0.48$50,000 0.24 0.38 0.45 0.49 0.50


This part of the chapter describes various accident modification factors that are related to thedesign of a rural intersection. The discussion is separated into AMFs that apply to signalizedintersections and those that apply to unsignalized intersections.

Rural Signalized Intersections

This section identifies the AMFs that are applicable to signalized intersections in a ruralenvironment. These factors were either derived from the models described in the previous sectionor extracted from other safety prediction models described in the literature. The focus of thediscussion is on AMFs related to geometric design; however, AMFs related to access control andother intersection features are also described.

Geometric Design

This subsection describes AMFs related to the geometric design of a rural signalizedintersection. Topics specifically addressed are listed in Table 6-7. Many geometric designcomponents or elements are not listed in this table (e.g., approach grade) that are also likely to havesome correlation with severe crash frequency. However, a review of the literature did not revealuseful quantitative information describing these effects. The list of available AMFs for intersectiongeometric design is likely to increase as new research in this area is undertaken.



Table 6-7. AMFs Related to Geometric Design of Rural Signalized Intersections.Section Accident Modification Factor

Cross section Left-turn lane Right-turn lane Number of lanesAlignment skew angle Intersection sight distance

In some instances, an AMF is derived from a safety prediction model as the ratio of“intersection crash frequency with a changed condition” to “intersection crash frequency without thechange.” In other instances, the AMF is obtained directly from a before-after study. Occasionally,crash rates reported in the literature were used to derive an AMF.

Left-Turn Lane. Harwood et al. (6) investigated the relationship between the presence ofleft- and right-turn lanes and crash frequency. They examined the change in severe crash frequencyat intersections that had a left-turn lane installed using a before-after study design. The results oftheir investigation are summarized in Table 6-8. The values shown in this table can be used toestimate the change in crashes at a signalized intersection at which a left-turn lane is added to oneor both of the major-road approaches.

Table 6-8. Effect of Adding a Left-Turn Lane at a Rural Signalized Intersection.

Number ofIntersection Legs

Number of Major-Road Approaches with Left-Turn Lanes InstalledOne Approach Both Approaches 3

All Crashes Severe Crashes All Crashes Severe Crashes3 0.85 0.86 1 not applicable4 0.82 0.83 2 0.67 0.69

Notes:1 - Value estimated as: 0.83 = 0.91/ 0.90 × 0.82 using urban intersection data reported by Harwood et al. (6).2 - Value estimated as: 0.86 = 0.91/ 0.90 × 0.85 using urban intersection data reported by Harwood et al. (6).3 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

The crash rates presented in a previous part of this chapter reflect typical rural signalizedintersection design. Data provided by Bauer and Harwood (4) indicate that the typical (i.e., base)condition for signalized intersections is “left-turn lane provided.” The values presented in Table 6-8have been converted to equivalent AMFs to reflect this base condition. The resulting left-turn laneAMFs are listed in Table 6-9.

Table 6-9. AMFs for Excluding a Left-Turn Lane at a Rural Signalized Intersection.


Number of Major-Road Approaches without Left-Turn Lanes InstalledOne Approach Both Approaches

All Crashes Severe Crashes All Crashes Severe Crashes3 1.18 1.16 not applicable4 1.22 1.21 1.49 1.45



Right-Turn Lane. Harwood et al. (6) also investigated the relationship between right-turnlanes and signalized intersection crash frequency. Their recommended AMFs for the addition of aright-turn lane on the major-road approach to a signalized intersection are shown in Table 6-10.Harwood et al. recommend using these AMFs for any signalized intersection, regardless whether ithas three or four legs.

Table 6-10. AMFs for Adding a Right-Turn Lane at a Rural Signalized Intersection.


Number of Major-Road Approaches with Right-Turn Lanes InstalledOne Approach Both Approaches 2

All Crashes Severe Crashes All Crashes Severe Crashes3 0.96 1 0.91 1 not applicable4 0.96 0.91 0.92 0.83

Notes:1 - Harwood et al. (6) did not quantify AMFs for signalized intersections with three legs. They recommend the

application of the “four-leg” AMFs to intersections with three legs.2 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

Number of Lanes on the Major and Minor Roads. A series of safety prediction modelswas developed by Bauer and Harwood (4) for rural and urban, signalized and unsignalizedintersections. A variable in these models relates the number of through lanes on the major and minorroads to the reported severe crash frequency. The regression coefficients in these models are shownin column 5 of Table 6-11. The AMF for each coefficient b can be computed as AMF = eb. Thus,the coefficient of -0.163 in the first row corresponds to an AMF of 0.85. It indicates that urbansignalized intersection approaches where the major-street has “3 or fewer” lanes will have 85 percentof the crashes experienced by approaches with “6 or more” lanes. Similar comparisons of the effectof number-of-lanes can be made within the other combinations of area type, control mode, and roadlisted.

The coefficients in column 5 were normalized for a common base number-of-lanes tofacilitate comparison across the various combinations of area type, control mode, and road. The basenumber of lanes used for this analysis is two through lanes. The normalized coefficients are listedin column 6. These values have similar interpretation as to those in column 5, the only differencebeing that the coefficients in column 6 have a “two-lane approach” as the base condition.Examination of the normalized coefficients indicates that the effect of number-of-lanes varies bycontrol mode. Specifically, an increase in lanes at a signalized intersection is associated with anincrease in severe crash frequency, all other factors unchanged. In contrast, an increase in lanes atan unsignalized intersection is associated with a decrease in severe crash frequency.



b ' c0 % (c1 % c2 Isg ) (Nln & 2) (6-21)

Table 6-11. AMFs for Number of Through Lanes at Rural and Urban Intersections.AreaType

ControlMode

Road Number ofThrough Lanes

RegressionCoefficient

NormalizedCoefficient 1

EstimatedCoefficient 2

AdjustedAMFlane

3

Urban Signalized Major 3 or fewer -0.163 0.000 0.000 0.994 or 5 -0.151 0.012 0.014 1.00

6 or more 0.000 0.163 0.029 1.01Minor 3 or fewer -0.155 0.000 0.000 1.00

4 or more 0.000 0.155 0.014 1.01Unsignalized Major 3 or fewer 0.282 0.000 0.000 1.20

4 or 5 0.049 -0.233 -0.185 1.006 or more 0.000 -0.282 -0.371 0.83

Minor 3 or fewer n.a. n.a. 0.000 1.004 or more n.a. n.a. -0.185 0.83

Rural Signalized Major 3 or fewer n.a. n.a. 0.000 1.004 or 5 n.a. n.a. 0.014 1.01

6 or more n.a. n.a. 0.029 1.03Minor 3 or fewer n.a. n.a. 0.000 1.00

4 or more n.a. n.a. 0.014 1.01Unsignalized Major 3 or fewer 0.385 0.000 0.000 1.00

4 or 5 0.000 -0.385 -0.185 0.836 or more n.a. n.a. -0.371 0.69

Minor 3 or fewer n.a. n.a. 0.000 1.004 or more n.a. n.a. -0.185 0.83

Notes:n.a. - data not available.1 - Normalized Coefficient: regression coefficient adjusted to yield a coefficient of 0.0 for two through lanes for all

combinations of area type, control mode, and road. Computed as bi ! b2; where, bi is the coefficient for combinationi and b2 is the coefficient for the two-lane case.

2 - Estimated Coefficient: normalized coefficient estimated using the calibrated regression model.3 - Adjusted AMF: estimated coefficient adjusted for number of lanes for the base condition (i.e., rural: 2 lanes major,

2 lanes minor; urban: 4 lanes major, 2 lanes minor) and converted to an AMF using AMF = e(estimated coefficient).

Regression analysis was used to identify the factors that influence the normalizedcoefficients. After separate evaluation of all factors, the regression model having the best fitincluded only an indicator variable to account for the effect of control mode. The form of this modelis:

where:Isg = indicator variable for control mode (1 if signalized; 0 if unsignalized); and

Nln = number of through lanes on the road.

Weighted regression was used for the analysis. The weight w assigned to each variable isequal to the reciprocal of the coefficient squared (i.e., wi = 1/bi

2). The calibrated model form is:



b ' (&0.093 % 0.100 Isg ) (Nln & 2) (6-22)

AMFnd ' e b (dn & 3) (6-23)

b ' c0 % c1 Isg (6-24)

Both constants in Equation 6-22 are statistically significant at a 99 percent confidence level. Theweighted coefficient of determination R2 of the regression model is 0.99.

As a last step, the estimated coefficients obtained from Equation 6-22 were adjusted to a basecondition number-of-lanes reflective of a rural intersection. The base condition for rural signalizedintersections is two lanes on both the major and minor roads. The AMF values appropriate for theseintersections are listed in rows 12 through 16 of column 8 in Table 6-11 (highlighted in bold font).

Alignment Skew Angle. Harwood et al. (3) found that intersection skew angle wascorrelated with intersection crash frequency at unsignalized intersections. However, intersectionskew apparently was not found to be related to crash frequency at signalized intersections. Harwoodet al. recommended an AMFskew of 1.0 (no effect) for intersection skew angle at signalizedintersections.

Intersection Sight Distance. Harwood et al. (3) convened an expert panel to determine therelationship between crash frequency and intersection sight distance at signalized intersections. Thepanel concluded that sight distance restrictions at a signalized intersection would not significantlyinfluence crash frequency. They recommended an AMFSD equal to 1.0 for signalized intersections.

Access Control

Several safety prediction models have been developed for rural intersections that include avariable that relates driveway frequency to crash frequency. Driveway frequency was defined to bethe count of driveways within 250 ft of the intersection on the major road. This count would includedriveways on both sides of the road and on both major-road intersection legs. The regressioncoefficients in these models are shown in column 6 of Table 6-12. The AMF for each coefficientb can be computed as:

where:AMFnd = driveway frequency accident modification factor; and

dn = number of driveways on the major road within 250 ft of the intersection.

This equation reflects a base condition of three driveways. The coefficients listed in Table 6-12consistently indicate an increase in crash frequency with an increase in driveway frequency,regardless of the control mode, driveway type, or number of intersection legs.

Regression analysis was used to identify the factors that influence the coefficient values.After separate evaluation of all factors, the regression model having the most logical fit included anindicator variable to account for the effect of control mode. The form of this model is:



b ' 0.056 & 0.010 Isg (6-25)

AMFnd ' e 0.046 (dn & 3) (6-26)

Table 6-12. Coefficient Analysis for Driveway Frequency at Rural Intersections.ControlMode

DrivewayType 1

IntersectionLegs

Model Source CrashSeverity

RegressionCoefficient


Signalized Any 4 Harwood et al. (3) All 0.041 0.046Comm. 4 Washington et al. (7) All 0.0539 0.046

Unsignalized Any 4 Harwood et al. (3) All 0.13 0.056Any 3 Vogt (2) All 0.0391 0.056Any 4 Washington et al. (7) All 0.1219 0.056

Comm. 3 Washington et al. (7) All 0.0681 0.056Notes: 1 - Driveway Type: Any - all driveway types (e.g., commercial, residential, industrial, etc.); Comm.- only commercial.2 - Estimated Coefficient: normalized coefficient estimated using the calibrated regression model.

Trends in the coefficients in column 6 of Table 6-12 suggest that there is a possible influenceof “number of legs” on the value of the coefficient b. However, the effect represented in thesecoefficients suggests that the addition of a fourth intersection leg increases the AMF value by a factorof 2.0 or more. This amount of increase is rationalized to be excessive and is likely due tocolinearity in the coefficients derived from the models for four-leg unsignalized intersections.



The constant “0.011” in Equation 6-25 is statistically significant at an 80 percent confidence level.The weighted coefficient of determination R2 of the regression model is 0.76. The coefficient forsignalized intersections is obtained from Table 6-12 (or Equation 6-25) as 0.046. This value can becombined with Equation 6-23 to obtain the following AMF for driveway frequency:

Figure 6-4 illustrates the driveway frequency AMF for rural, four-leg signalized intersections.The two AMFs obtained from the coefficients reported by Harwood et al. (3) and by Washington etal. (7) are shown with thin trend lines. The AMF obtained from Equation 6-26 is shown with a thickbold line (and labeled “derived”). The trends shown in the figure are in general agreement andsuggest that an intersection with no driveways within 250 ft will have an AMF of about 0.87 andimplies that it will be associated with 13 percent fewer crashes than an intersection with threedriveways (say, two driveways on one major-road approach and one on the other approach).



AMFtk ' e b (Pt & 9) (6-27)

AMFtk ' e 0.028(Pt & 9) (6-28)

0.6

0.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5 6

Driveways within 250 ft of Intersection

Acc

iden

t Mod

ifica

tion

Fact

or

Derived

Harwood et al. (3)

Washington et al. (7)

Figure 6-4. Driveway Frequency AMF for Rural Signalized Intersections.


This section describes AMFs related to features of the signalized intersection that are notcategorized as related to geometric design or access control. Specifically, the AMFs described inthis section address truck presence and speed.

Truck Presence. Vogt (2) and Harwood et al. (3) both found a relationship between crashfrequency and truck presence at signalized intersections on rural highways. Each researcherdeveloped a safety prediction model that includes various factors (including truck percentage). TheAMF that is derived from these models is shown below. It reflects a base condition of 9 percenttrucks.

where:AMFtk = truck presence accident modification factor, and

Pt = percent trucks during the peak hour (average for all intersection movements), %.

The value of variable b is shown in Table 6-13 for the two referenced sources. Also shownis the weighted average of the two coefficients. The weighted average can be used with Equation 6-27 to obtain the following AMF for truck presence:



AMFsl ' e b (V & 55) (6-29)

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15

Truck Percentage, %

Acc

iden

t Mod

ifica

tion

Fact

or

Harwood et al. (3)

Vogt (2)Derived

Table 6-13. Coefficient Analysis for Truck Presence at Rural Signalized Intersections.Model Source Intersection Type Crash Severity Coefficient b

Vogt (2) Rural 4-leg signalized intersection Severe 0.0323Harwood et al. (3) Rural 4-leg signalized intersection All 0.026

Weighted Average: 1 0.028Note:1 - Weighted average computed as: 0.028 = (1/0.0323 + 1/0.026) / (1/0.03232 + 1/0.0262 ).

Figure 6-5 illustrates the two expressions for the truck presence AMF that are based on themodels developed by Vogt (2) and by Harwood et al. (3). The AMF obtained from Equation 6-28is shown with a thick bold line (and labeled “derived”). The trends shown suggest that anintersection with no trucks has an AMF of about 0.77. Thus, this intersection will be associated with23 percent fewer crashes than an intersection with 9 percent trucks. Trucks have a more difficulttime stopping in response to the change in signal indication than passenger cars. This fact, coupledwith the high-speed nature of most rural signalized intersections, is likely to result in more truck-involved rear-end and right-angle crashes as truck percentage increases.

Figure 6-5. Truck Presence AMF for Rural Signalized Intersections.

Speed. Several safety prediction models have been developed that include a variable thatrelates speed limit or design speed to crash frequency. The regression coefficients in these modelsare shown in column 7 of Table 6-14. The AMF associated with each coefficient b can be derivedusing Equation 6-29. This equation reflects a base speed of 55 mph.

where:AMFsl = speed accident modification factor; and

V = major-road speed limit (or design speed), mph.



b ' c0 % c1 Iurb (6-30)

b ' 0.019 & 0.014 Iurb (6-31)

AMFsl ' e 0.019 (V & 55) (6-32)

Table 6-14. Coefficient Analysis for Speed at Rural and Urban Intersections.AreaType

ControlMode

RoadType

IntersectionLegs

SpeedType 1

Model Source RegressionCoefficient 2


Urban Signalized Major 4 Design Bauer & Harwood (4) 0.005 0.005Rural Signalized Major 4 Limit Washington et al. (7) 0.0397 0.019

Unsignal-ized

Major 4 Design Bauer & Harwood (4) 0.013 0.019Minor 4 Limit Vogt (2) 0.0339 0.019Minor 4 Limit Washington et al. (7) 0.0289 0.019

Notes:1 - Speed type: type of speed used to calibrate the regression coefficient (i.e., design speed, or speed limit).2 - All coefficients listed are derived from models relating speed to severe crash frequency. 3 - Estimated Coefficient: normalized coefficient estimated using the calibrated regression model.

An examination of the regression coefficients listed in Table 6-14 indicated a consistent trendtoward an increase in crash frequency with an increase in either the speed limit or the design speed.Regression analysis was used to determine if area type, control mode, road type, number ofintersection legs, or speed type was correlated with the coefficient values. Based on this analysis,the following model was found to offer the best fit to the data:

where:Iurb = indicator variable for area type (1 if urban; 0 if rural).



The constants in Equation 6-31 are statistically significant at a 94 percent confidence level. Theweighted coefficient of determination R2 of the regression model is 0.80. The coefficient for ruralsignalized intersections is obtained from Table 6-14 (or Equation 6-31) as 0.019. It is equallyapplicable to speed limit or design speed. This value can be combined with Equation 6-29 to obtainthe following AMF for speed:

Figure 6-6 illustrates the speed AMF for rural signalized intersections. The AMF obtainedfrom the coefficient reported by Washington et al. (7) is shown with the thin trend line. The AMFobtained from Equation 6-32 is shown with a thick bold line (and labeled “derived”). The trends inthe two AMFs indicate that lower speeds are associated with fewer severe crashes. These AMFswere derived from severe crash data. Hence, the trends found likely reflect the increase in crashseverity with increasing speed.



0.4

0.6

0.8

1.0

1.2

1.4

40 45 50 55 60 65 70

Speed, mph

Acc

iden

t Mod

ifica

tion

Fact

or


Derived

Figure 6-6. Speed AMF for Rural Signalized Intersections.

Rural Unsignalized Intersections

This section identifies the AMFs that are applicable to unsignalized intersections in a ruralenvironment. Specifically, these are two-way stop-controlled intersections. The factors identifiedwere either derived from the models described previously or extracted from other safety predictionmodels described in the literature. The focus of the discussion is on AMFs related to geometricdesign; however, AMFs related to access control and other intersection features are also described. Geometric Design

This subsection describes AMFs related to the geometric design of a rural unsignalizedintersection. Topics specifically addressed are listed in Table 6-15. Many geometric designcomponents or elements are not listed in this table (e.g., approach grade) that are also likely to havesome correlation with severe crash frequency. However, a review of the literature did not revealuseful quantitative information describing these effects. The list of available AMFs for intersectiongeometric design is likely to increase as new research in this area is undertaken.

Table 6-15. AMFs Related to Geometric Design of Rural Unsignalized Intersections.Section Accident Modification Factor

Cross section Left-turn lane Right-turn lane Number of lanesShoulder width Median presence Alignment skew angleIntersection sight distance

In some instances, an AMF is derived from a safety prediction model as the ratio of“intersection crash frequency with a changed condition” to “intersection crash frequency without the



change.” In other instances, the AMF is obtained directly from a before-after study. Occasionally,crash rates reported in the literature were used to derive an AMF.

Left-Turn Lane. Harwood et al. (6) investigated the relationship between the presence ofleft- and right-turn lanes and crash frequency. They examined the change in severe crash frequencyat intersections that had a left-turn lane installed using a before-after study design. The results oftheir investigation are summarized in Table 6-16. The values shown in this table can be used toestimate the change in crashes at unsignalized intersections at which a left-turn lane is added to oneor both of the major-road approaches.

Table 6-16. AMFs for Adding a Left-Turn Lane at a Rural Unsignalized Intersection.


Number of Major-Road Approaches with Left-Turn Lanes InstalledOne Approach Both Approaches 1


Note:1 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

The crash rates presented in a previous part of this chapter reflect typical rural signalizedintersection design. Data provided by Bauer and Harwood (4) indicate that the typical (i.e., base)condition for rural unsignalized intersections is “no left-turn lane provided.” The values presentedin Table 6-16 reflect this base condition.

Right-Turn Lane. Harwood et al. (6) also investigated the relationship between right-turnlane presence and unsignalized intersection crash frequency. Their recommended AMFs for theaddition of a right-turn lane on the major-road approach to an unsignalized intersection are shownin Table 6-17. Harwood et al. recommend using these AMFs for any unsignalized intersection,regardless whether it has three or four legs.

Table 6-17. AMFs for Adding a Right-Turn Lane at a Rural Unsignalized Intersection.


Number of Major-Road Approaches with Right-Turn Lanes InstalledOne Approach Both Approaches 1


Note:1 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.



AMFsw ' e &0.030 (Ws & 8) (6-33)

Number of Lanes on the Major and Minor Roads. Bauer and Harwood (4) developedseveral safety prediction models that relate traffic and geometric factors to severe crash frequencyat rural unsignalized intersections. One of the factors included in several of their models was thenumber of through lanes on the major road. The coefficients in these models were used in aregression analysis to compute the AMFs listed in column 3 of Table 6-18. Details of this regressionanalysis are provided in the discussion associated with Table 6-11. The AMFs in Table 6-18 reflecta base condition of two through lanes on the major and minor roads.

Table 6-18. AMFs for Number of Through Lanes at Rural Unsignalized Intersections.Road Number of Through Lanes on

Major RoadAMFlane

Major 3 or fewer 1.004 or 5 0.83

6 or more 0.69Minor 3 or fewer 1.00

4 or more 0.83

Shoulder Width. Bauer and Harwood (4) developed several safety prediction models thatrelate outside shoulder width and other factors to severe crash frequency at rural, unsignalizedintersections. The AMF that is derived from these models is shown below. It reflects a baseshoulder width of 8 ft.

where:AMFsw = shoulder width accident modification factor; and

Ws = outside shoulder width, ft.

The regression coefficient of “-0.030” in Equation 6-33 was derived from a model for three-leg intersections. However, in the absence of information to the contrary, it is believed to be equallyapplicable to four-leg intersections.

Figure 6-7 illustrates the shoulder width AMF. The trend line shown suggests that 5 ftshoulders are associated with an AMF of 1.09 and implies that intersections with 5 ft shouldersexperience 9 percent more crashes than those with 8 ft shoulders, all other factors unchanged.

Median Presence and Width. Bauer and Harwood (4) developed a safety prediction modelfor three-leg unsignalized intersections that includes a variable relating the presence of a median onthe major road to the reported total crash frequency. The regression coefficients in this model wereused to compute the relative effect of median presence on crash frequency. The computed AMFsare shown in column 3 of Table 6-19. These AMFs reflect the base condition of an undivided majorroad. In the absence of research to the contrary, this AMF is believed to be equally applicable tointersections with four legs.



AMFmw ' e b (Wm & 16) (6-34)

AMFmw ' e &0.012(Wm & 16) (6-35)

0.4

0.6

0.8

1.0

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10

Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

3-Leg & 4-Leg Intersections

Figure 6-7. Shoulder Width AMF for Rural Unsignalized Intersections.

Table 6-19. AMFs for Median Presence at Rural Unsignalized Intersections.Model Source Median Type on Major Road AMFmp, base

Bauer & Harwood (4) Divided 0.73Undivided 1.00

Additional research on the relationship between intersection median width and crashfrequency has also been conducted by Vogt (2), Washington et al. (7), and Harwood et al. (8). Allthree research efforts found a relationship between crash frequency and median width at unsignalizedintersections on rural highways. Each researcher developed a safety prediction model that includesvarious factors (including median width). The AMF that is derived from these models is shownbelow. It reflects a 16 ft median width as the base condition.



The value of variable b is shown in Table 6-20 for the three referenced sources. Also shownis the weighted average of the coefficients applicable to “all” crash severities. The weighted averagecan be used with Equation 6-34 to obtain the following AMF for median width:



AMFmp ' AMFmp,base × AMFmw (6-36)

0.2

0.4

0.6

0.8

1.0

1.2

15 20 25 30 35 40

Median Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

4-Leg IntersectionHarwood et al. [8])3-Leg Intersection

(Vogt [2])

3-Leg Intersection(Washington et al. [7]) 3-Leg & 4-Leg Ints.

(derived)

Table 6-20. Coefficient Analysis for Median Width at Rural Unsignalized Intersections.Model Source Road Intersection Legs Crash Severity Coefficient b

Vogt (2) Major 3 All -0.0546Washington et al. (7) Major 3 All -0.0106Harwood et al. (8) Major 4 All -0.0122

Major 4 Severe -0.0135Weighted Average: 1 -0.012

Note:1 - Weighted average computed as: -0.012 = (-1/0.0546 ! 1/0.0106 ! 1/0.0122) / (1/0.05462 + 1/0.01062 + 1/0.01222).

Figure 6-8 illustrates the three expressions for the median width AMF that are based on themodels listed in Table 6-20 for “all” crash severities. The AMF obtained from Equation 6-35 isshown with a thick bold line (and labeled “derived”). It is coincident with the trend obtained fromthe Harwood et al. (8) model. The trends shown suggest that an intersection with a 25 ft median hasan AMF of about 0.90, which implies that it will be associated with 10 percent fewer crashes thanan intersection with a 16 ft median.

Figure 6-8. Median Width AMF for Rural Unsignalized Intersections.

In application, the base median presence and median width AMFs should be used togetherto evaluate the likely change in crash frequency due to introduction of a median in the vicinity of anunsignalized intersection. Both of these AMFs were developed using crash data reflecting all crashseverities; however, the trends are rationalized to be applicable to severe crashes as well. Thefollowing equation demonstrates the manner by which the two AMFs should be combined:

If a left-turn bay is present, AMFmp, base should equal 1.0.



AMFskew ' e b Isk (6-37)

AMFskew 'e 0.019 Isk if 3 legs

e 0.021 Isk if 4 legs(6-38)

Alignment Skew Angle. Vogt (2), Harwood et al. (3), and Washington et al. (7) developedsafety prediction models that relate skew angle and other factors to total crash frequency at ruralunsignalized intersections. The AMF that is derived from these models is shown below. It reflectsa base condition of no skew (i.e., a 90-degree intersection).

where:AMFskew = skew angle accident modification factor, and

Isk = skew angle of the intersection, degrees.

Skew angle is defined as the absolute value of the difference between the intersection angleand 90 degrees (i.e., Isk = | intersection angle ! 90 |). By this definition, skew angle is always apositive quantity when the two roads intersect at other than a 90 degree angle.

The values of b to be used with Equation 6-37 are listed in Table 6-21. The weighted averagefor severe crashes at three-leg intersections is computed from the two referenced models and equals0.019. The weighted average for “all” crash severities is also computed and equals 0.0048. Theratio of these two values suggests that b is about four times larger for severe crashes than it is for“all” crash severities. This ratio was used to estimate the value of b for severe crashes at four-legintersections as 0.021. The estimated values are used to derive the following skew angle AMF:

Table 6-21. Coefficient Analysis for Skew Angle at Rural Unsignalized Intersections.Model Source Intersection Legs Crash Severity Coefficient b

Vogt (2) 3 Severe 0.023Harwood et al. (3) 3 All 0.0040

Washington et al. (7) 3 Severe 0.0163All 0.0101

Weighted Average: 1 Severe 0.019All 0.0048

Harwood et al. (3) 4 All 0.0054Severe 0.021 2

Note:1 - Weighted average computed as: 0.019 = (1/0.023 + 1/0.0163) / (1/0.0232 + 1/0.01632); 0.0048 = (1/0.004 +

1/0.0101) / (1/0.004 + 1/0.01012).2 - Estimated as: 0.021 = 0.0054 × 0.019/0.0048.



AMFskew,4 ' 1 %0.048 Isk

0.72 % 0.048 Isk(6-39)

0.8

1.0

1.2

1.4

1.6

1.8

0 5 10 15 20 25 30

Intersection Skew Angle, degrees

Acc

iden

t Mod

ifica

tion

Fact

or

3-Leg Intersection

Vogt (2)Derived


0.8

1.0

1.2

1.4

1.6

1.8

0 5 10 15 20 25 30

Intersection Skew Angle, degrees

Acc

iden

t Mod

ifica

tion

Fact

or

4-Leg Intersection


Derived

Washington et al. (7) developed an AMF for skew angle at four-leg intersections; however,its formulation did not follow that of Equation 6-37. Their AMF is:

This equation was derived using severe crash data.

Figure 6-9 illustrates the two expressions for the skew angle AMF. The trend lines shownsuggest that a three-leg intersection with 30 degrees of skew is associated with an AMF of 1.74 andimplies that intersections with no skew experience 57 percent (=1/1.74) fewer crashes than thosewith 30 degrees of skew, all other factors unchanged. The AMF derived for four-leg intersectionsis consistent with that developed by Washington et al. (7) (i.e., Equation 6-39). Additional researchis needed to determine which functional form is most appropriate. In the interim, Equation 6-38 isrationalized to offer the more reasonable estimate of the relationship between skew and crashfrequency at four-leg intersections.

a. Three-Leg Intersections. b. Four-Leg Intersections.

Figure 6-9. Skew Angle AMF for Rural Unsignalized Intersections.

Intersection Sight Distance. During the development of AMFs for rural two-lane highways,Harwood et al. (3) convened an expert panel to determine the relationship between crash frequencyand intersection sight distance deficiencies. Sight distance was considered to be “limited” if theavailable sight distance was less than that specified by AASHTO policy for a speed of 10 mph lessthan the major-road design speed. The AASHTO policy in reference is published in A Policy onGeometric Design of Highways and Streets (9).

The expert panel determined that crash frequency would increase by 5 percent for eachintersection quadrant that had limited intersection sight distance. Thus, if two quadrants had limitedsight distance, AMFSD would be equal to 1.10 (= 1.00 + 0.05 × 2).



AMFnd ' e b dn (6-40)

AMFnd ' e 0.056 dn (6-41)

Access Control

Several safety prediction models have been developed for rural intersections that include avariable that relates driveway frequency to crash frequency. Driveway frequency was defined to bethe count of driveways within 250 ft of the intersection on the major road. This count would includedriveways on both sides of the road and on both major-road intersection legs. The regressioncoefficients in these models are shown in column 6 of Table 6-12. The AMF for each coefficientb can be computed as:

where:AMFnd = driveway frequency accident modification factor; and

dn = number of driveways on the major road within 250 ft of the intersection.

This equation reflects a base condition of no driveways. The coefficients listed in Table 6-12consistently indicate an increase in crash frequency with an increase in driveway frequency,regardless of the control mode, driveway type, or number of intersection legs.

An analysis of the various coefficients in Table 6-12 indicates that the coefficient forunsignalized intersections is 0.056. This value can be combined with Equation 6-40 to obtain thefollowing AMF for driveway frequency:

Figure 6-10 illustrates the driveway frequency AMF for signalized intersections. The AMFsobtained from the coefficients reported by other researchers are shown with thin trend lines. TheAMF obtained from Equation 6-41 is shown with a thick bold line (and labeled “derived”). TheAMF trend lines attributed to others suggest that there is a possible influence of “number of legs”on the value of the AMF. However, the trends shown suggest that the addition of a fourthintersection leg increases the AMF value by a factor of 2.0 or more. This amount of increase isrationalized to be excessive and is likely due to colinearity in the coefficients derived from themodels for four-leg unsignalized intersections.



1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6

Driveways within 250 ft of Intersection

Acc

iden

t Mod

ifica

tion

Fact

or3-Leg & 4-Leg Intersections (derived)

4-Leg Intersection(Harwood et al. [3])

3-Leg Intersection(Vogt [2])

4-Leg Intersection(Washington et al. [7])

AMFtk ' e b (Pt & 9) (6-42)

AMFtk ' e &0.030(Pt & 9) (6-43)

Figure 6-10. Driveway Frequency AMF for Rural Unsignalized Intersections.


This section describes AMFs related to features of the unsignalized intersection that are notcategorized as related to geometric design or access control. Specifically, the AMFs described inthis section addresses truck presence and speed.

Truck Presence. Washington et al. (7) found a relationship between crash frequency andtruck presence at unsignalized intersections on rural highways. They developed a safety predictionmodel that includes a factor representing truck percentage. The AMF that is derived from thesemodels is shown below. It reflects a base condition of 9 percent trucks.

where:AMFtk = truck presence accident modification factor, and

Pt = percent trucks during the peak hour (average for all intersection movements), %.

The value of variable b is shown in Table 6-22. Also shown is the weighted average of thetwo coefficients. The weighted average can be used with Equation 6-42 to obtain the followingAMF for truck presence:



AMFsl ' e b (V & 55) (6-44)

0.6

0.8

1.0

1.2

1.4

1.6

0 5 10 15

Truck Percentage, %

Acc

iden

t Mod

ifica

tion

Fact

or

4-Leg IntersectionWashington et al. (7)

3-Leg IntersectionWashington et al. (7)

3-Leg & 4-Leg Intersections(derived)

Table 6-22. Coefficient Analysis for Truck Presence at Rural Unsignalized Intersections.Model Source Intersection Legs Crash Severity Coefficient b

Washington et al. (7) 3 Severe -0.02534 Severe -0.0520

Weighted Average: 1 -0.030Note:1 - Weighted average computed as: -0.030 = (-1/0.0253 ! 1/0.0520) / (1/0.02532 + 1/0.05202 ).

Figure 6-11 illustrates the two expressions for the truck presence AMF that are based on themodels developed by Washington et al. (7). The AMF obtained from Equation 6-43 is shown witha thick bold line (and labeled “derived”). The derived trend suggests that an intersection with notrucks has an AMF of about 1.30, which implies that it will be associated with 30 percent morecrashes than an intersection with 9 percent trucks. This relationship between truck presence andAMF value is similar to that found for urban street segments. It is likely that an increase in trucksdoes not make the intersection safer; rather, it probably indicates that drivers are more cautious whenthere are many trucks in the traffic stream.

Figure 6-11. Truck Presence AMF for Rural Unsignalized Intersections.

Speed. Several safety prediction models have been developed for rural and urbanintersections that include a variable that relates speed limit or design speed to crash frequency. Theregression coefficients in these models were shown previously in Table 6-14. The AMF for eachcoefficient b can be computed as:

where:



AMFsl ' e 0.019 (V & 55) (6-45)

0.4

0.6

0.8

1.0

1.2

1.4

40 45 50 55 60 65 70

Speed, mph

Acc

iden

t Mod

ifica

tion

Fact

or


Derived

Vogt (2)

Bauer & Harwood (4)

AMFsl = speed accident modification factor; and V = major-road speed limit (or design speed), mph.

This equation reflects a base speed of 55 mph. The coefficient for rural unsignalized intersectionsis obtained from Table 6-14 as 0.019. This value can be combined with Equation 6-44 to obtain thefollowing AMF for speed:

Figure 6-12 illustrates the speed AMF for rural unsignalized intersections. The AMFsobtained from the coefficients reported by other researchers are shown with the thin trend line. TheAMF obtained from Equation 6-45 is shown with a thick bold line (and labeled “derived”). Thetrends in the two AMFs indicate that lower speeds are associated with fewer severe crashes. TheseAMFs were derived from severe crash data. Hence, the trends found likely reflect the increase incrash severity with increasing speed.

Figure 6-12. Speed AMF for Rural Unsignalized Intersections.

REFERENCES


2. Vogt, A. Crash Models for Rural Intersections: Four-Lane by Two-Lane Stop Controlled andTwo-Lane by Two-Lane Signalized. Report No. FHWA-RD-99-128. Federal HighwayAdministration, Washington, D.C., October 1999.



3. Harwood, D., F. Council, E. Hauer, W. Hughes, and A. Vogt. Prediction of the Expected SafetyPerformance of Two-Lane Highways. Report No. FHWA-RD-99-207. Federal HighwayAdministration, Washington, D.C., December 2000.

4. Bauer, K., and D. Harwood. Statistical Models of At-Grade Intersections–Addendum. ReportNo. FHWA-RD-99-094. Federal Highway Administration, Washington, D.C., March 2000.

5. Vogt, A., and J. Bared. Accident Models for Two-Lane Rural Roads: Segments andIntersections. Report No. FHWA-RD-98-133. Federal Highway Administration, Washington,D.C., October 1998.

6. Harwood, D., K. Bauer, I. Potts, D. Torbic, K. Richard, E. Kohlman Rabbani, E. Hauer, andL. Elefteriadou. Safety Effectiveness of Intersection Left- and Right-Turn Lanes. Report No.FHWA-RD-02-089. Federal Highway Administration, Washington, D.C., July 2002.

7. Washington, S., B. Persaud, C. Lyon, and J. Oh. Validation of Accident Models forIntersections. Report No. FHWA-RD-03-037. Federal Highway Administration, Washington,D.C., July 2005.

8. Harwood, D., M. Pietrucha, K. Fitzpatrick, and M. Wooldridge. “Design of Intersections onDivided Highways.” TRB Circular E-C003: International Symposium on Highway GeometricDesign Practices. Transportation Research Board, Washington, D.C., 1998, Chapter 29, pp.1-14.

9. A Policy on Geometric Design of Highways and Streets. American Association of StateHighway and Transportation Officials, Washington, D.C., 2004.

Chapter 7 Urban Intersections


Chapter 7Urban Intersections

Page


SAFETY PREDICTION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5Urban Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5

Lyon Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5Bauer and Harwood Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8McGee Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9Comparison of Signalized Intersection Crash Models . . . . . . . . . . . . . . . . . . . . . . . . . 7-10

Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11Bauer and Harwood Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11McGee Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-13Comparison of Unsignalized Intersection Crash Models . . . . . . . . . . . . . . . . . . . . . . 7-14

Development of Representative Intersection Crash Rates . . . . . . . . . . . . . . . . . . . . . . . . . 7-15

ACCIDENT MODIFICATION FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18Urban Signalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18

Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18Left-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18Right-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19Number of Lanes on the Major and Minor Streets . . . . . . . . . . . . . . . . . . . . . . . . 7-19Lane Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-20

Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-21Urban Unsignalized Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-22

Geometric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-22Left-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-23Right-Turn Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24Number of Lanes on the Major and Minor Streets . . . . . . . . . . . . . . . . . . . . . . . . 7-24Lane Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24Shoulder Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26Median Presence and Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26

Other Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-28

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29



INTRODUCTION

Intersections are a necessary consequence of a surface street system. They represent the pointwhere two streets cross and thus, are points of significant potential conflict. On a statewide basis,more than one-half of all crashes in urban areas occur at intersections. The safe operation of anintersection requires the use of traffic control devices to separate the conflicting movements in time.These devices typically include yield sign, stop sign, or traffic signal. The geometric design of theintersection and the type of traffic control devices used (and, if signal control is used, the signalphasing and timing) have a significant effect on the safety and operation of the intersection. Theaccommodation of automobile, truck, pedestrian, and bicycle travel modes presents unique designchallenges in the urban environment, and especially at intersections. The high cost of right-of-wayin urban areas can present an additional challenge to intersection design.

The development of a safe, efficient, and economical urban intersection design may reflectconsideration of a wide variety of design alternatives. A variety of techniques exist for estimatingthe operational benefits of alternatives; many are automated through software tools. Techniques forestimating construction and right-of-way costs are also available to the designer. Unfortunately,techniques for estimating the safety benefits of alternative designs are not as readily available. Thischapter summarizes information in the literature that can be used to estimate the crash frequencyassociated with various urban intersection design alternatives.

Objective

The objective of this chapter is to synthesize information in the literature that quantitativelydescribes the relationship between various urban intersection design components and safety. Thisinformation is intended to provide a basis for the development of a procedure for estimating thesafety benefit of alternative designs. This procedure is documented in Chapter 7 of the RoadwaySafety Design Workbook (1).

The presentation consists of an examination of safety prediction models and accidentmodification factors (AMFs). Safety prediction models provide an estimate of the expected crashfrequency for a typical urban intersection. They include variables for the volume of the conflictingtraffic streams. They also include variables for other factors considered to be correlated with crashfrequency (e.g., median type, functional class, etc.). One or more AMFs can be multiplied by theexpected crash frequency obtained from the prediction model to produce an estimate of the expectedcrash frequency for a specific intersection.

Scope

This chapter addresses the safety of intersections in an urban area. As such, the crash typesused to describe the level of safety are identified as “intersection related.” The intersectionrelationship of a crash is indicated on the crash report or, in some instances, is determined by theresearchers. If the researchers determine the intersection-relationship of a crash, it is oftentimesbased on crash location relative to the intersection. Specifically, all crashes that occur within aspecified distance back from the intersection are labeled as “intersection related.” The combination



of crash location and type (e.g., turn related or multi-vehicle) has also been used by some researchersto identify intersection relationship. Crashes that are not intersection related are referred to hereinas “mid-block” crashes and are the subject of Chapter 4.

When available, safety relationships that estimate the frequency of severe (i.e., injury or fatal)crashes are given preference for inclusion in this document. This preference is due to a widevariation in reporting threshold among cities and states. This variation complicates the extrapolationof crash trends found in one location to another location. Moreover, it can confound thedevelopment of safety prediction models using data from multiple agencies. Reporting thresholdis strongly correlated with the number of property-damage-only (PDO) crashes found in a crashdatabase. Agencies with a high reporting threshold include relatively few PDO crashes in theirdatabase and vice versa. As a consequence, the total crash frequency for a given intersection willbe high if it is located in a city with a low reporting threshold. This problem is minimized whencrash data analyses, comparisons, and models are based on data pertaining only to severe crashes.

The relationships described in this chapter address the occurrence of vehicle-related crashesat urban intersections. They assume that the distribution of pedestrian and bicycle crashes remainsunchanged, regardless of the change in design or traffic volume. Relationships that specifically focuson vehicle-pedestrian and vehicle-bicycle crashes on streets are not addressed.

Overview

This chapter documents a review of the literature related to urban intersection safety. Thefocus is on quantitative information that relates severe crash frequency to various geometric designcomponents of the urban intersection. The review is not intended to be comprehensive in the contextof referencing all relevant works that discuss urban intersection safety. Rather, the informationpresented herein is judged to be the most current information that is relevant to urban street designin Texas. It is also judged to be the most reliable based on a review of the statistical analysistechniques used and the explanation of trends.


This chapter is envisioned to be useful to design engineers who desire a more completeunderstanding of the relationship between various intersection design components and severe crashfrequency. As noted previously, it is also intended to serve as the basis for the development of thesafety evaluation procedure described in Chapter 7 of the Roadway Safety Design Workbook (1).

This chapter consists of two main parts. In the first part to follow, several safety predictionmodels reported in the literature are described. In the second part, accident modification factors aredescribed for various geometric design and traffic control components. In each of these parts, thereis a separate discussion of signalized and unsignalized intersections.



Ci ' α Qβ1major Q

β2minor e (β3 Qminor) (7-1)


Described in this part of the chapter are several safety prediction models that were developedto estimate the expected frequency of intersection-related crashes. The discussion is separated intotwo sections with one section describing models that apply to signalized intersections and a secondsection describing models that apply to unsignalized intersections. At the end of each section, themodels are compared in terms of the relationship between severe crash frequency and traffic volume.

All of the models presented in this part of the chapter make reference to the “major” and“minor” streets that form the intersection. These models are based on the assumption that the “majorstreet” is the street with the higher volume of the two streets. It most instances, this assumption isin agreement with the number of lanes provided and the functional class of the two streets.However, in some instances, this assumption may mean that a street with more lanes or a higherfunctional classification but with lower volume will need to be specified as the “minor” street forthe purpose of using a safety prediction model.

Urban Signalized Intersections

This section addresses safety prediction models for urban signalized intersections. Three setsof models are described and are identified by the names of their developers. They include:

! Lyon Models! Bauer and Harwood Models! McGee Models

Lyon Models

Lyon et al. (2) created a family of safety prediction models specifically for urban signalizedintersections. The intersections in their database are located in the city of Toronto in Ontario,Canada. Separate models were developed for various combinations of intersection legs andfunctional classification of the intersecting streets. The following generalized model form was usedfor all combinations:

where:Ci = frequency of severe intersection-related crashes at intersections with leg and

classification combination i, crashes/yr;Qmajor = total daily volume on major street (both directions), veh/d;Qminor = total daily volume on minor street (both directions), veh/d; andα, βj = regression coefficients (j = 1, 2, 3).

Table 7-1 lists the values of α and βj for each combination of intersection legs and functionalclass. Also listed are the coefficient values for an “overall” model for the three-leg and the four-legintersection categories. This overall model is based on the full database, independent of thefunctional class of the intersecting streets.



Table 7-1. Calibration Coefficients for Lyon Models.Number of

Intersection LegsFunctional Classification Model Calibration Coefficients

Major Street Minor Street α β1 β2 β3

4 Local Local 0.000531 0.434 0.382 0.00000947Minor arterial Local 0.000877

Collector 0.000992Minor arterial 0.001458

Major arterial Local 0.001087Collector 0.001347Minor arterial 0.001549Major arterial 0.001632

Any Any 0.000082 0.570 0.545 0.000006043 a Minor arterial,

collector, localMinor arterial,collector, local

0.000204 0.588 0.375 0.0

Major arterial Local 0.000160Collector 0.000232Minor or major arterial 0.000251

Any Any 0.000063 0.598 0.503 0.0Note:a - Values of α were multiplied by 0.5β2 to convert minor-street volume from “entering volume” to “leg volume.”

As Table 7-1 shows, the β1, β2, and β3 values are the same for all functional classcombinations of four-leg intersections (except when using all combinations) and for all functionalclass combinations of three-leg intersections. Only the value for α varies among the variousfunctional classes.

Figures 7-1 and 7-2 illustrate the predicted severe crash frequency for the family of modelsdeveloped by Lyon et al. (2). As the legend in each figure indicates, a ratio of major to minorvolume has been specified to facilitate the comparison of the various models. The ratio used forfour-leg intersections is 0.2 and that for three-leg intersections is 0.1. These ratios are typical ofmost intersections between a major arterial and a minor arterial or collector street.

The trends shown in Figures 7-1 and 7-2 indicate that the functional class of the intersectingstreets is correlated with severe crash frequency. In general, intersections where the major street isclassified as a major arterial and the minor street is classified as a major arterial, minor arterial, orcollector experience more crashes than intersections where the major street is classified as a minorarterial, collector, or local. This finding suggests that intersections on streets that are functionallymore “important” tend to experience more crashes than intersections on less important streets. It islikely a reflection of the more complex design and signalization environment (e.g., channelized turnlanes, left-turn phases, etc.) associated with “important” intersections. It may also reflect thelikelihood that “important” intersections often operate more nearly at their capacity during manyhours of the day. Lengthy delays and, possibly, congestion result in more dense traffic flows andincreased driver anxiety that could lead to a reduction in the overall level of intersection safety.



0

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0 15 30 45 60

Major-Street Volume (1000's), veh/d

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Minor/MinorMinor/CollectorMinor/LocalLocal/Local

Major/MajorMajor/MinorMajor/CollectorMajor/LocalAll Classes


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Major/MajorMajor/Minor

All Classes

Minor/MinorMinor/CollectorMinor/LocalLocal/Local

Major/CollectorMajor/Local


Figure 7-1. Crash Models Developed by Lyon et al. for Four-Leg Intersections.

Figure 7-2. Crash Models Developed by Lyon et al. for Three-Leg Intersections.

A supplemental examination was conducted that explored the relationship between crashfrequency and the number of intersection legs. To facilitate this examination, the volume ratio wasset to a common value of 0.2. On streets where the major street is classified as a major arterial, thetrends shown indicate that three-leg intersections tend to experience about 70 to 90 percent of thecrashes that four-leg intersections experience, all other factors being the same. In contrast, on streetswhere the major street is classified as a minor arterial, collector, or local street; three-legintersections experience about the same crash frequency as four-leg streets.



C ' 0.001066 Q 0.574major Q 0.215

minor e B1 % B2 (7-2)

B1 ' &0.051 Ipt % 0.400 Ifa & 0.240 Imp & 0.290 Iac (7-3)

B2 ' &0.155 Imin & 0.163 Imaj3 & 0.151 Imaj4 % 0.005 Vd (7-4)

The characteristics of the data used by Lyon et al. (2) are summarized in Table 7-2. Theyused five years of crash data for each of 1716 urban intersections. The researchers defined allcrashes occurring at, or within 65 ft of, the intersection as “intersection related.”

Table 7-2. Database Characteristics for Signalized Intersection Safety Prediction Models.Model




IntersectionLegs


Lyon et al. (2) City of Toronto 5 65 ft 3 3064 1410

Bauer &Harwood (3)

California Dept. ofTransportation

3 250 ft 4 1342

McGee et al.(4)


8 not available 3 1704 629




Bauer and Harwood (3) investigated the relationships between crash frequency and variousintersection geometry and operational attributes. They developed a series of safety prediction modelsfor a variety of intersection configurations and control conditions. The model they developed forfour-leg urban signalized intersections is described in this subsection. The models they developedfor three-leg and four-leg urban unsignalized intersections are discussed in a later section. The ruralintersection models are described in Chapter 6.

Bauer and Harwood’s model for predicting severe crash frequency at four-leg urbansignalized intersections is:

with,

and

where:C = frequency of severe intersection-related crashes, crashes/yr;Ipt = control type indicator variable (1 if intersection is pretimed; 0 if semi-actuated);Ifa = control type indicator variable (1 if intersection is fully actuated; 0 if semi-actuated);

Imp = signal phasing indicator variable (1 if more than 2 phases; 0 otherwise);Imin = minor-street through lanes (1 if 3 or fewer lanes; 0 otherwise);



Iac = major-street access control indicator variable (1 if no access control; 0 if partial control);Imaj3 = major-street through lanes (1 if 3 or fewer lanes; 0 otherwise);Imaj4 = major-street through lanes (1 if 4 or 5 lanes; 0 otherwise); and

Vd = major-street design speed, mph.

It should be noted that the model predicts fewer crashes when the major street does not haveaccess control, relative to one with partial access control. No justification or rationale was offeredby the researchers for this counter-intuitive trend.

The characteristics of the data used by Bauer and Harwood (3) are summarized in Table 7-2.As this table indicates, their models are based on three years of crash data for each of 1342 urbanintersections. In contrast to Lyon et al. (2), Bauer and Harwood defined intersection-related crashesto be all crashes that occurred at, or within 250 ft of, the intersection.

McGee Models

McGee et al. (4) developed a series of safety prediction models for urban intersections.Collectively, the intersections represented five states and Canada. The vast majority of the data wereobtained from the California Department of Transportation. They used the generalized equationshown previously in Equation 7-1 to develop models based solely on the California data. Thecalibration coefficients for the signalized intersection models are listed in Table 7-3. The calibratedmodel predicts the frequency of severe crashes.

Table 7-3. Calibration Coefficients for McGee Signalized Intersection Models.Number of

Intersection LegsModel Calibration Coefficients

α β1 β2 β3

4 0.003180 0.4911 0.1975 0.03 a 0.000480 0.6370 0.1901 0.0

Note:a - Value of α was multiplied by 0.5β2 to convert minor-street volume from “entering volume” to “leg volume.”

As indicated by the data in Table 7-3, separate models were calibrated to the three-leg andfour-leg intersections in the database. Although not apparent by inspection of the coefficients listedin the table, examination of model predictions indicates that three-leg intersections have between 60and 80 percent of the crashes experienced by four-leg intersections, for similar volume levels. Thisfinding is generally consistent with the trend noted previously for the Lyon et al. (2) model.

A second model was developed by McGee et al. (4) using the crash data for the other states(and Canada) combined; however, this model is not described herein because it does not distinguishbetween three-leg and four-leg intersections. The findings noted in the previous paragraph indicatethat such a distinction should have been found in the combined database.



The characteristics of the data used by McGee et al. (4) are listed in Table 7-2. As indicatedin the table, their models are based on eight years of crash data for each of 799 urban intersections.The researchers did not indicate the method they used to identify intersection-related crashes.

Comparison of Signalized Intersection Crash Models

The models described in the previous subsections are compared in this subsection. Theobjective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. The models were grouped into three-leg and four-leg categories.For the Bauer and Harwood (3) model, the values of the other model variables were set at typicalvalues for urban signalized intersections. These values are listed in Table 7-4.

As the information in Table 7-4 indicates, only the Bauer and Harwood model includedvariables related to the design or operation of the intersection. The typical values listed are basedon the median values for each variable in the California database, as described by Bauer andHarwood (3, Table 18).

Table 7-4. Typical Values Used for Urban Signalized Intersection Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

Lyon et al. (2) Bauer & Harwood (3)

McGee et al.(4)

Signal control fully actuated -- U --Access control none -- U --Signal phasing more than 2 phases -- U --Number of lanes on major street 4 -- U --Number of lanes on minor street 2 -- U --Design speed, mph 50 -- U --

Figure 7-3 illustrates the crash frequency predictions obtained from the various models.Bauer and Harwood did not develop a model for three-leg signalized intersections. The trendsshown indicate a general agreement that the annual severe crash frequency for the four-legintersections tends to equal between 4 and 6 crashes/yr when the major-street volume is60,000 veh/d. The three-leg intersection trend lines exhibit a little more variability and suggest thatsevere crashes number between 3 and 5 crashes/yr for a similar volume level.

The trend lines shown in Figure 7-3 for Lyon et al. are consistently above those for McGeeet al. and for Bauer and Harwood. This trend suggests that drivers in the city of Toronto (i.e., fromwhich the Lyon data were obtained) are more inclined to have severe crashes than those in the stateof California (from which the McGee and the Bauer and Harwood data were obtained). However,it could also be explained by possible differences in the definition of an injury crash. A review ofcrash data from five states (including California) and Toronto by McGee et al. (4) confirms that



C ' 0.003053 Q 0.584major Q 0.206

minor e B1 % B2 (7-5)

B1 ' &0.081 Wl & 0.747 Ilt & 0.382 Iac & 0.079 Ima & 0.401 Icl (7-6)

0

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Lyon et al. (2)Major/Collector

McGee et al (4)

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Lyon et al. (2)Major/Collector

McGee et al (4)

Bauer & Harwood (3)Full actuatedNo access controlThree phasesTwo lanes on minorFour lanes on major50 mph design speed

severe crash rates at four-leg intersections in Toronto are 20 percent larger than in California(40 percent larger for three-leg intersections). This finding is consistent with the trends in Figure7-3. It should also be noted that crash rates in the other four states are even larger than that foundin Toronto.


Figure 7-3. Comparison of Safety Prediction Models for Urban Signalized Intersections.

Urban Unsignalized Intersections

This section addresses safety prediction models for urban unsignalized intersections.Specifically, these are two-way stop-controlled (TWSC) intersections. Two sets of models aredescribed and are identified by the names of their developers. They include:

! Bauer and Harwood Models! McGee Models


Bauer and Harwood (3) investigated the relationships between crash frequency and variousintersection geometry and operational attributes. They developed a series of safety prediction modelsfor a variety of intersection configurations and control conditions. The models they developed forthree-leg and four-leg urban TWSC intersections are discussed in this subsection. The ruralintersection models are described in Chapter 6.

Bauer and Harwood’s model for predicting severe crash frequency at urban four-leg TWSCintersections is:

with,



C ' 0.000445 Q 0.696major Q 0.238

minor e B1 % B2 (7-8)

B1 ' &0.048 Wl & 0.393 Ilt & 0.581 Ifrt & 0.057 Inoltln % 0.209 Icbltln (7-9)

B2 ' & 0.182 Idiv % 0.094 Inolite (7-10)

B2 ' 0.282 Imaj3 % 0.049 Imaj4 & 0.020 Ws & 0.300 Ifrt (7-7)

and


Wl = major-street lane width, ft;Ilt = major-street left-turn control indicator variable (1 if left turns are prohibited; 0 otherwise);Iac = major-street access control indicator variable (1 if no access control; 0 partial control);Ima = major-street functional class indicator variable (1 if minor arterial; 0 if principal arterial);Icl = major-street functional class indicator variable (1 if collector; 0 if principal arterial);

Imaj3 = major-street through lanes (1 if 3 or fewer lanes; 0 otherwise);Imaj4 = major-street through lanes (1 if 4 or 5 lanes; 0 otherwise);Ws = major-street outside shoulder width, ft; andIfrt = minor-street channelization (1 if no free right-turn lane; 0 if free right-turn lane).

It should be noted that the model predicts fewer crashes when the major street does not haveaccess control, relative to one with partial access control. No justification or rationale was offeredby the researchers for this counter-intuitive trend.

Bauer and Harwood’s model for predicting severe crash frequency at urban three-leg TWSCintersections is:

with,

and


Inoltln = major-street left-turn channelization indicator variable (1 if no left-turn lane; 0 if paintedleft-turn lane);

Icbltln = major-street left-turn channelization indicator variable (1 if curbed left-turn lane; 0 ifpainted left-turn lane);

Idiv = major-street median indicator variable (1 if divided; 0 if undivided); andInolite = intersection lighting indicator variable (1 if no lighting; 0 otherwise).

It should be noted that the model predicts fewer crashes on a major street that does not haveleft-turn channelization and more crashes on one that has curbed channelization. This trend wouldseem counter-intuitive. No justification or rationale was offered by the researchers for this counter-intuitive trend.

Although not apparent by inspection of the coefficients listed in Equations 7-5 through 7-10,an examination of model predictions indicates that three-leg intersections have between 50 and



65 percent of the crashes experienced by four-leg intersections, for similar volume levels. Thisfinding is generally consistent with the trend noted previously for the signalized intersection models.

The characteristics of the data used by Bauer and Harwood (3) are summarized in Table 7-5.They used three years of crash data for each of 4399 urban intersections. The researchers definedall crashes occurring at, or within 250 ft of, the intersection as “intersection related.”

Table 7-5. Database Characteristics for Unsignalized Intersection Safety Prediction Models.Model




IntersectionLegs


Bauer &Harwood (3)


3 250 ft 3 30574 1342

McGee et al.(4)


8 not available 3 9394 479

California, Florida,Maryland, Virginia,Wisconsin, Toronto

varies,4 to 10

not available 3 99

4 199



McGee Models

McGee et al. (4) developed a series of safety prediction models for urban intersections.Collectively, the intersections represented five states and Canada. The vast majority of the data wereobtained from the California Department of Transportation (DOT). They used the generalizedequation shown previously in Equation 7-1 to develop their models. They developed one set ofmodels using the California DOT database and a separate set using the mix of states and Canada.The calibration coefficients for the unsignalized intersection models they developed are listed inTable 7-6. The calibrated model predicts the frequency of severe crashes.

Table 7-6. Calibration Coefficients for McGee Unsignalized Intersection Models.Data Source Number of

Intersection LegsModel Calibration Coefficients

α β1 β2 β3

California DOT 3 a 0.000146 0.7032 0.2011 0.04 0.000340 0.6188 0.2946 0.0

California, Florida,Maryland, Virginia,Wisconsin, Toronto

3 a 0.0000011 0.968 0.558 0.0

4 0.000426 0.499 0.430 0.0

Note:a - Value of α was multiplied by 0.5β2 to convert minor-street volume from “entering volume” to “leg volume.”



As indicated by the data in Table 7-6, separate models were calibrated to the three-leg andfour-leg intersections in the database. Although not apparent by inspection of the coefficients listedin the table, examination of model predictions based on the “California DOT” data indicates thatthree-leg intersections have 55 percent of the crashes experienced by four-leg intersections. Thisfinding is generally consistent with the trend noted previously for the Bauer and Harwoodunsignalized models and for the signalized intersection models. In contrast, this trend is not as stablein the model predictions based on the five states plus Toronto. A comparison of these two modelsindicates that three-leg intersections have between 35 and 105 percent of the crashes of the four-legintersections. This wide variation is not explained by McGee et al. nor is it apparent in the crashrates quoted in their research report (4, Table 4). A detailed examination of these crash ratesindicates that three-leg intersections have about 70 percent of the crashes experienced by four-legintersections–a trend that is consistent with that found in previous models.

The characteristics of the data used by McGee et al. (4) are summarized in Table 7-5. As thistable indicates, their “California DOT” models are based on eight years of crash data for each of1418 unsignalized intersections. Their other two models are based on data from several states (andToronto) and collectively represent 298 intersections. The researchers did not indicate the methodthey used to identify intersection-related crashes.

Comparison of Unsignalized Intersection Crash Models

The models described in the previous subsections are compared in this subsection. Theobjective of this comparison is to determine which model or models are reasonable in theirprediction of severe crash frequency. To facilitate this comparison, the models are examined overa range of traffic volume levels. The models were grouped into three-leg and four-leg categories.For the Bauer and Harwood (3) model, the values of the model variables were set at typical valuesfor urban unsignalized intersections. These values are listed in Table 7-7.

Table 7-7. Typical Values Used for Urban Unsignalized Intersection Model Comparison.Model Variable Typical Value Safety Prediction Model Developer

McGee et al. (4) Bauer & Harwood (3)Lane width, ft 12 -- U

Shoulder width, 1 ft 1.5 -- U

Access control none -- U

Left-turn operation on major street allowed -- U

Number of lanes on major street 4 -- U

Free right-turn lanes on minor street no -- U

Median type (divided, undivided) undivided street -- U

Left-turn channelization on major street painted bay -- U

Intersection lighting yes -- U

Note:1 - It is assumed that curb-and-gutter is provided on the typical urban street instead of a shoulder. This cross section

is assumed to have an equivalent “shoulder” width of 1.5 ft.



0.0

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McGee et al (4): Five State Mix "California DOT"

Bauer & Harwood (3)12 ft lane widthNo shoulderFour lanes on majorLeft-turns allowedNo access controlNo free right-turn lanesMajor arterial

CR '106

365α Q

β1major Q

β2minor

Qmajor % Qminor

(7-11)

0.0

0.5

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2.0

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Bauer & Harwood (3)12 ft lane widthLeft-turns allowedNo access controlNo free right-turn lanesUndivided streetLeft-turn channelizationLighting provided

McGee et al (4): Five State Mix"California DOT"

As the information in Table 7-7 indicates, only the Bauer and Harwood model includedvariables related to the design or operation of the intersection. The typical values listed are basedon the median values for each variable in the California database, as described by Bauer andHarwood (3, Tables 10 and 14).

Figure 7-4 illustrates the crash frequency predictions obtained from the various models. Thetrends shown indicate a general agreement that the annual severe crash frequency for four-legintersections tends to equal between 1.3 and 2.3 crashes/yr when the major-street volume is30,000 veh/d.


Figure 7-4. Comparison of Safety Prediction Models for Urban Unsignalized Intersections.

The three-leg intersection trend lines collectively exhibit more variability than the four-legmodels. As noted previously, the model developed by McGee et al. for three-leg intersections usingthe “five state” database yielded an illogical trend relative to four-leg intersection crash frequencies.This model is shown using a dashed trend line in Figure 7-4b. There appears to be some unexplainedartifact in this model that cannot be explained by other models or by examination of the crash ratesreported by the models’ developers.

Development of Representative Intersection Crash Rates

The safety prediction models previously presented are examined more closely in this sectionfor the purpose of developing representative intersection crash rates. To obtain the desired crash rateequation, Equation 7-1 was divided by the sum of entering flow and then multiplied by a conversionconstant to obtain the traditional crash rate units–crashes per million entering vehicles. The resultingcrash rate formula is:

with,



α ' αb % e (β3 Qminor % other terms ) (7-12)

CR ' 2740α Q

β1 % β2 & 1major r β2

1 % r(7-13)

R2 = 0.88

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

-12.0 -10.0 -8.0 -6.0 -4.0

alpha

b1 +

b2 -

1

α ' e &13.7 % 1.58 Nleg (7-14)

R2 = 0.52

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-12.0 -10.0 -8.0 -6.0 -4.0

alpha

b2

Stop controlSignal control

where:CR = severe crash rate for intersection-related crashes, crashes/million-vehicle-miles (mvm);α = regression constant that combines αb with all exponential terms at their average value; andαb = regression constant obtained from multivariate regression model.

Equation 7-11 was simplified to the following form by substituting the ratio of the minor-street to major-street entering flows r:

where:r = ratio of minor-street to major-street daily volumes (= Qminor / Qmajor).

As a next step in the examination, the relationship between α, β1, β2, and various variablesdescribing intersection control and number of approach legs was investigated. For this analysis, avariable alpha was computed as the natural log of α (i.e., alpha = ln[α]). Figure 7-5a illustrates therelationship found between alpha and the sum “β1 + β2 !1” (where β1 and β2 are labeled b1 and b2,respectively). Figure 7-5b illustrates the relationship found between α and β2. In general, the trendsillustrate that the variables alpha, β1, and β2 are correlated with each other and with the type of signalcontrol. A subsequent analysis indicated a similar correlation between alpha and the number ofintersection legs (R2 = 0.31).

a. Correlation between Alpha and “β1 + β2 !1.” b. Correlation between Alpha and β2.

Figure 7-5. Correlation between Model Coefficients.

The following relationships were derived based on the analysis of model coefficients:

with,



β1 % β2 & 1 ' &0.880 & 0.100 ln(α) (7-15)

β2 ' &0.729 % 0.120 Nleg % 0.137 Isig & 0.069 ln(α) (7-16)

and

where:Nleg = number of intersection legs (3 or 4); andIsig = indicator variable for intersection control mode (1 for signalized; 0 otherwise).

Equations 7-14, 7-15, and 7-16 were used with Equation 7-13 to compute equivalent crashrates for various combinations of intersection control and number of approach legs. The findingsfrom this analysis are presented in Tables 7-8 and 7-9. The rates listed in Table 7-8 are not sensitiveto major-street volume. This outcome was a consequence of Equations 7-14 and 7-15. The valueof “β1 + β2 !1” obtained from Equation 7-15 was equal to 0.014 for three-leg intersections. Thiseffectively eliminated the major-street flow variable in Equation 7-13 and produced the noted lackof sensitivity to major-street volume.

Table 7-8. Severe Crash Rates for Three-Leg Urban Intersections.ControlMode

Crash Rate, severe crashes per million-vehicle-milesRatio of Minor-Street to Major-Street Volume

0.05 0.10 0.15 0.20 0.25Unsignalized 0.18 0.21 0.22 0.22 0.23Signalized 0.12 0.15 0.17 0.18 0.19

Table 7-9. Severe Crash Rates for Four-Leg Urban Intersections.ControlMode

Major-Street Volume, veh/d

Crash Rate, severe crashes per million-vehicle-milesRatio of Minor-Street to Major-Street Volume

0.10 0.30 0.50 0.70 0.90Unsignalized 5000 0.25 0.29 0.28 0.27 0.26

10,000 0.23 0.26 0.26 0.25 0.2415,000 0.22 0.24 0.24 0.23 0.2220,000 0.21 Intersection very likely to meet signal warrants25,000 0.20

Signalized 5000 0.19 0.24 0.26 0.26 0.2610,000 0.17 0.22 0.23 0.23 0.2315,000 0.16 0.21 0.22 0.22 0.2220,000 0.15 0.20 0.21 0.21 0.2125,000 0.15 0.19 0.20 0.21 0.2030,000 0.14 0.19 0.20 0.20 0.2040,000 0.14 0.18 0.19 0.19 0.19$50,000 0.13 0.17 0.18 0.19 0.18



C ' CR 365106

(Qmajor % Qminor ) (7-17)

The following equation should be used to estimate severe crash frequency in conjunctionwith the crash rates listed in Tables 7-8 or 7-9:


This part of the chapter describes various accident modification factors that are related to thedesign of an urban intersection. The discussion is separated into AMFs that apply to signalizedintersections and those that apply to unsignalized intersections.

Urban Signalized Intersections

This section identifies the AMFs that are applicable to signalized intersections in an urbanenvironment. These factors were either derived from the models described in the previous sectionor extracted from other safety prediction models described in the literature. The focus of thediscussion is on AMFs related to geometric design; however, AMFs related to other intersectionfeatures are also described.

Geometric Design

This subsection describes AMFs related to the geometric design of an urban signalizedintersection. Topics specifically addressed are listed in Table 7-10. Many geometric designcomponents or elements are not listed in this table (e.g., approach grade) that are also likely to havesome correlation with severe crash frequency. However, a review of the literature did not revealuseful quantitative information describing these effects. The list of available AMFs for intersectiongeometric design is likely to increase as new research in this area is undertaken.

Table 7-10. AMFs Related to Geometric Design of Urban Signalized Intersections.Section Accident Modification Factor

Cross section Left-turn lane Right-turn lane Number of lanesLane width


Left-Turn Lane. Harwood et al. (5) investigated the relationship between the presence ofleft- and right-turn lanes and crash frequency. They examined the change in severe crash frequencyat intersections that had a left-turn lane installed using a before-after study design. The results of



their investigation are summarized in Table 7-11. The values shown in this table can be used toestimate the change in crashes at a signalized intersection at which a left-turn lane is added to oneor both of the major-street approaches.

Table 7-11. Effect of Adding a Left-Turn Lane at an Urban Signalized Intersection.


Number of Major-Street Approaches with Left-Turn Lanes InstalledOne Approach Both Approaches 2

All Crashes Severe Crashes All Crashes Severe Crashes3 0.93 0.94 1 not applicable4 0.90 0.91 0.81 0.83

Notes:1 - Data not available from Harwood et al. (5). Value estimated using “All Crash” data as: 0.94 = 0.91/ 0.90 × 0.93.2 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

The crash rates presented in a previous part of this chapter reflect typical urban signalizedintersection design. Data provided by Bauer and Harwood (3) indicate that the typical (i.e., base)condition for signalized intersections is “left-turn lane provided.” The values presented inTable 7-11 have been converted to equivalent AMFs to reflect this base condition. The resultingleft-turn lane AMFs are listed in Table 7-12.

Table 7-12. AMFs for Excluding a Left-Turn Lane at an Urban Signalized Intersection.


Number of Major-Street Approaches without Left-Turn LanesOne Approach Both Approaches


Right-Turn Lane. Harwood et al. (5) also investigated the relationship between right-turnlanes and signalized intersection crash frequency. Their recommended AMFs for the addition of aright-turn lane on the major-street approach to a signalized intersection are shown in Table 7-13.Harwood et al. recommend using these AMFs for any signalized intersection, regardless whether ithas three or four legs. It should be noted that the addition of a right-turn lane may reduce the safetyafforded to pedestrians, especially if the turn radius is large and turn speeds are high.

Number of Lanes on the Major and Minor Streets. Bauer and Harwood (3) developedseveral safety prediction models that relate the number of through lanes on the major and minorstreets to crash frequency. The coefficients in these models were used in a regression analysis tocompute the AMFs listed in column 3 of Table 7-14. Details of this regression analysis are providedin the discussion in Chapter 6 that is associated with Table 6-11. The AMFs in Table 7-14 reflecta base condition of four through lanes on the major street and two through lanes on the minor street.



AMFlw ' e &0.053 (Wl & 12) (7-18)

Table 7-13. AMFs for Adding a Right-Turn Lane at an Urban Signalized Intersection.


Number of Major-Street Approaches with Right-Turn Lanes InstalledOne Approach Both Approaches 2

All Crashes Severe Crashes All Crashes Severe Crashes3 0.96 1 0.91 1 not applicable4 0.96 0.91 0.92 0.83

Notes:1 - Harwood et al. (5) did not quantify AMFs for signalized intersections with three legs. They recommend the

application of the “four-leg” AMFs to intersections with three legs.2 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

Table 7-14. AMFs for Number of Through Lanes at Urban Signalized Intersections.Street Number of Through Lanes on

Major StreetAMFlane



4 or more 1.01

Lane Width. Bauer and Harwood (3) developed a safety prediction model that relatesseveral factors (including lane width) to total crash frequency (i.e., property-damage-only and severecrashes) at urban signalized intersections. The coefficient relating lane width to crash frequency isshown in the equation below. The base condition for this AMF is a 12 ft lane width. In the absenceof research to the contrary, this AMF is believed to be equally applicable to severe crashes.

where:AMFlw = lane width accident modification factor; and

Wl = lane width, ft.

Figure 7-6 illustrates the AMF for lane width. The trend line shown suggests that 9 ft trafficlanes are associated with an AMF of 1.17 and implies that intersections with 9 ft lanes experience17 percent more crashes than those with 12 ft lanes, all other factors unchanged.



AMFsl ' e b (V & 40) (7-19)

AMFsl ' e 0.005 (V & 40) (7-20)

0.6

0.8

1.0

1.2

1.4

1.6

9 9.5 10 10.5 11 11.5 12

Lane Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

Figure 7-6. Lane Width AMF for Urban Signalized Intersections.


This subsection describes AMFs related to features of the street that are not categorized asrelated to geometric design. The only AMF identified in the research that does not fit into these twocategories relates to speed. Several safety prediction models have been developed for rural andurban intersections that include a variable that relates speed limit or design speed to crash frequency.The regression coefficients in these models that provide this relationship are listed in Table 6-14 inChapter 6. They can be used with the following generalized equation to estimate the speed AMF:

where:AMFsl = speed accident modification factor; and

V = major-street speed limit (or design speed), mph.

This equation reflects a base speed of 40 mph.

Regression analysis was used to identify the factors that influence the coefficient values.After separate evaluation of all factors, the regression model having the best fit included an indicatorvariable to account for the effect of area type. The findings from this analysis are described inChapter 6. The coefficient for urban signalized intersections is obtained from Table 6-14 as 0.005.This value can be combined with Equation 7-19 to obtain the following AMF for speed:



0.4

0.6

0.8

1.0

1.2

1.4

25 30 35 40 45 50 55

Speed, mph

Acc

iden

t Mod

ifica

tion

Fact

or

Derived Bauer & Harwood (3)

Figure 7-7 illustrates the speed AMF for urban signalized intersections. The AMF obtainedfrom Equation 7-20 is shown with a thick bold line (and labeled “derived”). The AMF obtainedfrom the coefficient reported by Bauer and Harwood (3) is also shown but it is coincident with thethick trend line. The trends in the two AMFs indicate that lower speeds are associated with fewersevere crashes. These AMFs were derived from severe crash data. Hence, the trends found likelyreflect the increase in crash severity with increasing speed.

Figure 7-7. Speed AMF for Urban Signalized Intersections.

Urban Unsignalized Intersections

This section identifies the AMFs that are applicable to unsignalized intersections in an urbanenvironment. Specifically, these are two-way stop-controlled intersections. The factors identifiedwere either derived from the models described in a previous section or extracted from other safetyprediction models described in the literature. The focus of the discussion is on AMFs related togeometric design; however, AMFs related to other intersection features are also described. Geometric Design

This subsection describes AMFs related to the geometric design of an urban unsignalizedintersection. Topics specifically addressed are listed in Table 7-15. Many geometric designcomponents or elements are not listed in this table (e.g., approach grade) that are also likely to havesome correlation with severe crash frequency. However, a review of the literature did not revealuseful quantitative information describing these effects. The list of available AMFs for intersectiongeometric design is likely to increase as new research in this area is undertaken.



Table 7-15. AMFs Related to Geometric Design of Urban Unsignalized Intersections.Section Accident Modification Factor

Cross section Left-turn lane Right-turn lane Number of lanesLane width Shoulder width Median presence


Left-Turn Lane. Harwood et al. (5) investigated the relationship between the presence ofleft- and right-turn lanes and crash frequency. They examined the change in severe crash frequencyat intersections that had a left-turn lane installed using a before-after study design. The results oftheir investigation are summarized in Table 7-16. The values shown in this table can be used toestimate the change in crashes at unsignalized intersections at which a left-turn lane is added to oneor both of the major-street approaches.

Table 7-16. Effect of Adding a Left-Turn Lane at an Urban Unsignalized Intersection.


Number of Major-Street Approaches with Left-Turn Lanes InstalledOne Approach Both Approaches 2

All Crashes Severe Crashes All Crashes Severe Crashes3 0.67 0.65 1 not applicable4 0.73 0.71 0.53 0.50

Notes:1 - Data not available from Harwood et al. (5). Value estimated using “All Crash” data as: 0.65 = 0.71/ 0.73 × 0.67.2 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

The crash rates presented in a previous part of this chapter reflect typical urban signalizedintersection design. Data provided by Bauer and Harwood (3) indicate that the typical (i.e., base)condition for urban unsignalized intersections is “left-turn lane provided.” The values presented inTable 7-16 have been converted to equivalent AMFs to reflect this base condition. The resultingleft-turn lane AMFs are listed in Table 7-17.

Table 7-17. AMFs for Excluding a Left-Turn Lane at an Urban Unsignalized Intersection.


Number of Major-Street Approaches without Left-Turn Lanes InstalledOne Approach Both Approaches




AMFlw ' e b (Wl & 12) (7-21)

Right-Turn Lane. Harwood et al. (5) also investigated the relationship between right-turnlane presence and unsignalized intersection crash frequency. Their recommended AMFs for theaddition of a right-turn lane on the major-street approach to an unsignalized intersection are shownin Table 7-18. Harwood et al. recommend using these AMFs for any unsignalized intersection,regardless whether it has three or four legs.

Table 7-18. AMFs for Adding a Right-Turn Lane at an Urban Unsignalized Intersection.


Number of Major-Street Approaches with Right-Turn Lanes InstalledOne Approach 1 Both Approaches 1, 2


Notes:1 - Harwood et al. (5) did not quantify AMFs for urban unsignalized intersections. They recommend that the AMFs

developed for rural four-leg unsignalized intersections can also be used for urban unsignalized intersections.2 - AMFs for “Both Approaches” estimated as the square of the “One Approach” AMFs.

Number of Lanes on the Major and Minor Streets. Bauer and Harwood (3) developedseveral safety prediction models that relate the number of through lanes on the major and minorstreets to the reported severe crash frequency. The coefficients in these models were used in aregression analysis to compute the AMFs listed in column 3 of Table 7-19. Details of this regressionanalysis are provided in the discussion in Chapter 6 that is associated with Table 6-11. The AMFsin Table 7-19 reflect a base condition of four through lanes on the major street and two through laneson the minor street.

Table 7-19. AMFs for Number of Through Lanes at Urban Unsignalized Intersections.Street Number of Through Lanes on

Major StreetAMFlane



4 or more 0.83

Lane Width. Bauer and Harwood (3) developed several safety prediction models that relatelane width and other factors to severe crash frequency at unsignalized intersections. The AMF thatis derived from these models is shown below. It reflects a base condition of 12 ft lanes.

where:



AMFlw ' e &0.057(Wl & 12) (7-22)

0.6

0.8

1.0

1.2

1.4

1.6

9 9.5 10 10.5 11 11.5 12

Lane Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

4-Leg Intersection(Bauer & Harwood [3])

3-Leg Intersection(Bauer & Harwood [3])

3-Leg & 4-Leg Intersection(derived)

AMFlw = lane width accident modification factor; andWl = lane width, ft.

The value of variable b is shown in Table 7-20 for three-leg and four-leg intersections. Alsoshown is the weighted average of the two coefficients. The weighted average can be used withEquation 7-21 to obtain the following AMF for lane width:

Table 7-20. Coefficient Analysis for Lane Width at Urban Unsignalized Intersections.Number of

Intersection LegsIntersection Type Crash Severity Coefficient b

3 Urban unsignalized intersection Severe -0.0484 Urban unsignalized intersection Severe -0.081

Weighted Average: 1 -0.057Note:1 - Weighted average computed as: -0.057 = (-1/0.048 ! 1/0.081) / (1/0.0482 + 1/0.0812 ).

Figure 7-8 compares Equation 7-22 with the relationships derived from the Bauer andHarwood (3) models. The trend line associated with Equation 7-22 is labeled “derived.” The trendsshown suggest that 9 ft traffic lanes are associated with an AMF of about 1.18 and imply thatintersections with 9 ft lanes experience 18 percent more crashes than those with 12 ft lanes, all otherfactors unchanged.

Figure 7-8. Lane Width AMF for Urban Unsignalized Intersections.



AMFsw ' e &0.020 (Ws & 1.5) (7-23)

0.4

0.6

0.8

1.0

1.2

1.4

0 1 2 3 4 5 6 7 8

Shoulder Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or

3-Leg & 4-Leg Intersections

Shoulder Width. Bauer and Harwood (3) developed several safety prediction models thatrelate outside shoulder width and other factors to severe crash frequency at urban, unsignalizedintersections. The AMF that is derived from these models is shown below. It reflects a basecondition of curb-and-gutter, which is estimated to have an equivalent “shoulder” width of 1.5 ft.

where:AMFsw = shoulder width accident modification factor; and

Ws = outside shoulder width, ft.

The regression coefficient of “-0.020” in Equation 7-23 was derived from a model for four-leg intersections. However, in the absence of information to the contrary, it is believed to be equallyapplicable to three-leg intersections.

Figure 7-9 illustrates the shoulder width AMF. The trend lines shown suggest that 5 ftshoulders are associated with an AMF of 0.93 and imply that intersections with 5 ft shouldersexperience 7 percent fewer crashes than those with curb-and-gutter (assumed to equal a nominal1.5 ft shoulder width), all other factors unchanged.

Figure 7-9. Shoulder Width AMF for Urban Unsignalized Intersections.

Median Presence and Width. Equation 7-8 presents the safety prediction model developedby Bauer and Harwood (3) for three-leg unsignalized intersections. It includes an AMF that relatesthe presence of a median on the major street to the reported severe crash frequency. The regressioncoefficient in this model was used to compute the relative effect of median presence on crashfrequency. The computed AMFs are shown in column 3 of Table 7-21. These values wereconverted into the AMFs listed in column 3. These AMFs reflect the base condition of an undivided



AMFmw '

e b (Wm & 16) : if Wm > 16

1.0 : if Wm # 16(7-24)

major street. In the absence of research to the contrary, this AMF is believed to be equally applicableto intersections with four legs.

Table 7-21. AMFs for Median Presence at Urban Unsignalized Intersections.Model Source Median Type on Major Street AMFmp, base

Bauer & Harwood (3) Divided 0.83Undivided 1.00

Additional research on the relationship between intersection median width and crashfrequency has also been conducted by Harwood et al. (6). They found a relationship between crashfrequency and median width at signalized intersections on urban/suburban streets. The AMF thatis derived to represent the effect of median width found by Harwood et al. is shown below. Itreflects a 16 ft median width as the base condition.



The value of variable b is shown in Table 7-22 for the referenced source. The coefficientsapplicable to severe crashes are recommended for application with Equation 7-24 to obtain a medianwidth AMF for urban intersections. This equation is limited to median widths of more than 16 ft inrecognition of the range of median widths represented in the crash data analyzed by Harwood et al.(6). It indicates that crash frequency increases with increasing median width. This trend wasconfirmed by Harwood et al. (6) in a follow-up study of conflicts and other undesirable maneuverson the median roadway of wider intersections. Wide median roadways tend to be improperly usedby drivers and, when complicated by the high median roadway volume found in urban areas, resultin an increased propensity for multiple vehicle collision.

Table 7-22. Coefficient Analysis for Median Width at Urban Unsignalized Intersections.Model Source Road Intersection Legs Crash Severity Coefficient b

Harwood et al. (6) Major 3 All 0.0082Severe 0.0076 1

4 All 0.0173Severe 0.0160

Note:1 - Estimated as: 0.0076 = 0.016 × 0.0082/0.0173.



AMFmp ' AMFmp,base × AMFmw (7-25)

AMFsl ' e b (V & 40) (7-26)

0.6

0.8

1.0

1.2

1.4

1.6

5 10 15 20 25 30

Median Width, ft

Acc

iden

t Mod

ifica

tion

Fact

or



Figure 7-10 illustrates the relationship between median width and the median width AMFbased on severe crashes. The trends shown indicate that crash frequency increases with increasingmedian width, as discussed in the preceding paragraph. The trend lines suggest that a four-legintersection with a 25 ft median has an AMF of about 1.15, which implies that it will be associatedwith 15 percent more crashes than a four-leg intersection with a 16 ft median.

Figure 7-10. Median Width AMF for Urban Unsignalized Intersections.

In application, the base median presence and median width AMFs should be used togetherto evaluate the likely change in severe crash frequency due to introduction of a median in the vicinityof an unsignalized intersection. The following equation demonstrates the manner by which the twoAMFs should be combined:

If a left-turn bay is present, AMFmp, base should equal 1.0.


This section describes AMFs related to features of the unsignalized intersection that are notcategorized as related to geometric design. The only AMF found that does not fit into one of thesetwo categories is that related to speed. Several safety prediction models have been developed forurban intersections that include a variable that relates speed limit or design speed to crash frequency.The regression coefficients in these models were shown previously in Table 6-14 of Chapter 6. TheAMF for each coefficient b can be computed as:

where:



AMFsl ' e 0.005 (V & 40) (7-27)

0.4

0.6

0.8

1.0

1.2

1.4

25 30 35 40 45 50 55

Speed, mph

Acc

iden

t Mod

ifica

tion

Fact

or

Derived

AMFsl = speed accident modification factor; and V = major-street speed limit (or design speed), mph.

This equation reflects a base speed of 40 mph. The coefficient for urban unsignalized intersectionsis obtained from Table 6-14 as 0.005. This value can be combined with Equation 7-26 to obtain thefollowing AMF for speed:

Figure 7-11 illustrates the speed AMF for urban unsignalized intersections. The trend lineindicates that lower speeds are associated with fewer severe crashes. These AMFs were derivedfrom severe crash data. Hence, the trends found likely reflect the increase in crash severity withincreasing speed.

Figure 7-11. Speed AMF for Urban Unsignalized Intersections.

REFERENCES


2. Lyon, C., A. Haq, B. Persaud, and S. Kodama. “Development of Safety Performance Functionsfor Signalized Intersections in a Large Urban Area and Application to Evaluation of Left-TurnPriority Treatment.” Paper No. 05-2192. Presented at the Transportation Research Board 84th

Annual Meeting, Washington, D.C., January 2005.

3. Bauer, K., and D. Harwood. Statistical Models of At-Grade Intersections–Addendum. ReportNo. FHWA-RD-99-094. Federal Highway Administration, Washington, D.C., March 2000.



4. McGee, H., S. Taori, and B. Persaud. NCHRP Report 491: Crash Experience Warrant forTraffic Signals. National Cooperative Highway Research Program, Transportation ResearchBoard, Washington, D.C., 2003.

5. Harwood, D., K. Bauer, I. Potts, D. Torbic, K. Richard, E. Kohlman Rabbani, E. Hauer, andL. Elefteriadou. Safety Effectiveness of Intersection Left- and Right-Turn Lanes. Report No.FHWA-RD-02-089. Federal Highway Administration, Washington, D.C., July 2002.

6. Harwood, D., M. Pietrucha, K. Fitzpatrick, and M. Wooldridge. “Design of Intersections onDivided Highways.” TRB Circular E-C003: International Symposium on Highway GeometricDesign Practices. Transportation Research Board, Washington, D.C., 1998, Chapter 29, pp.1-14.

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